This walkthrough masterfully bridges the gap between abstract linear modeling and practical business logic with surgical precision. It is an essential guide that transforms intimidating exam patterns into clear, actionable mathematical intuition.
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CSEC Math Jan 2026 P3 EXTREMELY IN-DEPTHAdded:
All right, guys. Rejie here from Math Vibes and we're going to be looking at some January and June paper trees to help in the paper tree exam for June 2026. So, like I just let you know all you know that Israel vibes here and police staying quiet. I got knocky vibes, right? So, all you don't know the proceedings. Israel vibes here talk, make jokes and understand the max. So, let we dump let we drive straight into it.
Wait, I don't know why they're not seeing the screen. Uh, give a second. It's kind of weird.
Okay, nice. So, some things first. What do you need to know for the CEC maths paper tree? Does anybody know? Does anybody know what you need for the maths paper tree?
Anybody know? Yes, sir.
All right. So the max paper three could be any two questions really from the paper two any two and but these are the main ones main ones you should focus on.
You should focus on measurement and geometry algebra and functions statistics and data handling relations functions and graphs vectors and matrices consumer arithmetic investigation. If all you want take a screenshot of this now because these are the topics that will come for paper three. So take a screenshot now. If you had the screenshot and you're ready to move on, let me know.
>> Yeah, guys, I'm live on YouTube. Go check my on YouTube. Okay, I had the screenshot people. I was in the crash course that have the paper tree and I hear know Camille Akira. Well, Akira, you write a paper tree.
>> Yes, sir.
>> Okay. Well, take our screenshots.
So let's move straight into the January 2026 paper.
>> Okay, nice. So I need a volunteer. I don't know how it goes. So somebody give this a read.
>> Yeah, this a paper tree life, but it will benefit you for paper two topics as well. So I need somebody to give this a read.
Everybody so quiet for boy. I hit a vibes. Something wrong.
>> You want me read?
>> Yeah. Yeah. Get a read. Get a read.
All right. Blackton owns and operates a small business. He does plumbing mostly in the countryside. Out of a well stocked mobile unit, he does not have a fixed way in which he calculates the cost of a job. Blackton's clientele has increased and so he needs to develop a model that he can utilize to quickly determineing the cost of a job.
>> Wait boy. So this man had to learn some math >> information is provided to you.
>> Yeah boy.
>> Yeah. You see the man don't know any math got to learn some math. Watch watch watch. He does not have a fixed way in which he calculates the cost of our job.
But we going to calculate that for him.
So Muel talk to me. You have you observe anything from this information?
Um, just by looking at it, let me know if you observe anything.
>> We Okay, I see. I see your mute. I'm not hearing you anymore.
When we look at this information, guys, are they seen anything about it?
Probably like the rate at which it's increasing.
It could make um >> okay kind of shaky but essentially it looks like a linear relationship. And why am I saying that? If you look at the data in the table, the cost is going up by how much? I want a little look at it and tell me if you're seeing something in common. So like we have 130 210 290 370 450 530 610 so >> by 80 >> by 80 and Nikolai isn't all of them going up by 80.
>> Yes sir.
>> So you understand why I say that this was a linear relationship because it has a constant change. You know like a line has a fixed gradient. So we can see that we might have to plot a line. So let me follow understand that.
>> Yes sir.
Okay. Good. Are you seeing that the rate of change is the same for every single um entry in the rows? Are you seeing that? Okay. Good. Again that suggests a linear relationship.
So let's check out part A.
Plaxton must carry out an inspection for each job and must discuss findings and options with customers before he begins.
The inspection cost is fixed and is included in the final payment for a job.
Using the information provided, plot a graph of cost versus time on the grid shown below, where t represents the time taken in hours to complete a job and c represents the total cost of the job in dollars.
Now Nikolai I want to ask you something right just by looking at this table you're seeing that the cost is increasing by a by by a same number 80 80 right saying that 80 >> yes >> so what do you think would happen if I if I backtracked here what is 130us 80 130us 80 is anybody sir sir >> 130 - 80 would be 50 and what is 1 minus one I want somebody to tell me what is one minus one >> zero >> zero so at zero hours he would have charged what $50 >> $50 >> okay so let me try to connect all the dots here So we're seeing a linear relationship and we have length of a job in hours. Now as the hours increasing the cost is going up by $80.
But when we backtrack a bit you're seeing that 130 minus 80 is 50. So if you guys had to think right if you had to think after reading this piece of information what do you think that 50 has to do about what you think that 50 is?
that 50 if you had to figure it out.
>> Flat inspection rate.
>> I agree Nikki. Let me know if you're seeing that. So, Nikki, when you look at the table over here and you see that as the length of a job increases, the cost increases by $80. Let me know if you're seeing that.
>> Yes, sir.
>> Right. Now, if we were to take away 80 from 130, what would that be?
Yeah, that would be 50. And if you take away one from one, what would that be?
>> That would be 50.
>> What's one minus one?
>> Zero.
>> Ah, >> zero.
>> So, you think you could figure out what that means?
So, it's saying that zero hours is 50.
Hm.
>> So, and then probably the $80 is for the inspection.
>> Nah. Nah, the 80 $80.
>> Nah, the 80 wouldn't be for the inspection.
The 80 looks like it'd be for the job because Nikki, as the length increases, the cost is increasing by $80. So that 80 looks like the cost somebody is paying for per hour if you understand what I mean.
>> Yes. Yes.
>> So as you're saying with the time as the time increases what increases? As the time increases what increases there?
>> The money.
>> Yeah. The cost. The cost. And so if you guys had to say what do you think the hourly rate would be? If you had to guess, if you had to guess, just pure logic here, >> $80.
>> I would say $80. So, just from looking at this table, we could infer that the person has to like for every hour that goes by, you have to pay $80. Cool. And from the table, we saw that if you backtrack a bit and you take away 80 from 130, you're going to be 50. And that would imply zero hours. So, that zero hours is like a flat. Okay. The man didn't do any work yet, but he's still getting paid. And if you read this part over here, it says that um the inspection cost is fixed and is included in the final payment for a job. So Nikki, the inspection cost if somebody hear this um you know how AC men work or ners work.
>> Yeah. or like even sell like them laundry man and thing that's fix like the the machines you know like washer dryer and thing and they would charge a fee just to check it out and then they would start to fix it.
>> Yes.
>> Yes sir.
>> Good. So from the table alone I could infer that you know maybe he would have had to maybe you had to pay him $50 to inspect it and then if he decides to fix it every hour that goes by you had to pay him 80 80.
I could figure out all that just by looking at this table. And I could also figure out that this is a linear relationship. Why I saying that? Because the rate of change is the same. The cost going up by the same 80. So hope you guys understand that is a constant increase.
So >> yes, >> let me just try to understand this one more time. So I want a volunteer somebody see if you could explain this table for me. See if you could explain the table to me. So any volunteers any volunteers dry so okay I see Mel try to explain it.
>> Yeah.
>> So basically the table shows the the hourly rate for um a job of Blackton.
Um, so and referring to the information that we found earlier, his flat inspection rate starts at $50 and for each hour that goes by, his um, well, you're paying him for $80 for his work added on to the inspection.
That is it. So, if there's somebody that does not understand this, all they know are very patient. They just come ask me and I'll go over it as much time as I need to to make sure they understand.
That is the mission here.
So if anybody is confused by anything so far, this is your chance. Talk to them.
I don't bite. I have big teeth dancing.
I don't bite. Any volunteers?
I'm going call upon some people in the zoom. I see Michelle here. Akira, Cassidy, look my son. I see Lucas, Samir, Camille, Ambika.
So anyone of you guys, are any of you all confused by the table? Let me know.
>> No, sir.
So does everybody understand that as the time increases you have to pay an additional 80 and so for every hour you had to pay and you had to pay 80, right?
I wonder if I understand that.
>> Okay.
>> Yes sir >> sir.
>> And again if you backtrack if you backtrack 130 minus 80 will be 50. And if you backtrack here, 1 minus one is zero. So just by looking at the table, I could see that the inspection cost might be 50 and the hourly rate is $80. So using the information provided, plot a graph of cost versus time. Not a problem. So they want us to plot cost versus time. Which one are they mentioning first? Which one are they mentioning first? Cost.
>> Time. Cost.
>> So whichever one they mention first is going to go on which axis?
The XIS X the X ais no is the Y axis the Y sir.
>> Yeah yeah yeah is the Y. Physics people going to know that. Physics people have to know that. Yeah.
>> Whichever one they mention first is going to go on the Y axis. Whichever one that they mention second is going to go on the X axis. So I see a lot of you guys may have gotten that wrong.
So like here's a quick sketch. Could somebody tell me what I'd plot over here? Could somebody tell me what I would plot over there?
>> I would plot the cost over here. Okay.
And what would I plot over here? On the x axis?
>> Time.
>> Time.
>> So again guys, whichever one they tell me first, which axis I going to put on the y axis or the x axis?
>> Y.
>> Y axis.
>> Okay, good. Good. So let's do the question now. Let's do the question. So we recognize that we're going to put a graph of course on the y- axis versus time on the x axis. Great. So I've already So I've already prepared a graph here and I have the information. So somebody just remind me what going on the y axis or what going on the y axis.
>> Cost >> and cost is being measured in dollars.
Okay. What is going to go on the x axis?
>> Time.
>> Time.
>> Time. We're measuring time in what?
hours.
>> I do end this question like how you would do for physics because I think it's double revision. So in physics when you're writing your axis you need to state what you are measuring as well as it units. So I have cost on the y- axis and time on the x- axis. Great. Now here's a here's a piece of advice I would give my students. Cost goes on the y axis. So you see cost here put a y there. Length of length of a job. This is time and that goes on the x axis. So probably x above that. This is important because our point is made up of a what and a what value? Somebody tell me what is a point made up of? A point >> right? A point is made up of a x comma y value.
So the reason I wrote an x above time and a y above course is so that you could easily figure out your points.
So, is there anybody confused as to what I did so far? If you are, just tell me.
I'll run over the thing like road to kill.
Yeah. Confused.
>> I feel I have some people here that are real confused and they're not saying anything, you know. Um, Camille, Cassidy, Sadika, Ambika, Shanaya, Alen, Ra, Nishana, Shane, Natisha. I've seen some new people here.
Chameleia, how much are you guys? I understand everybody understand.
>> Okay, cool.
>> Yes, sir.
>> So, then somebody tell my first point um off guard.
>> Oh, sorry. Yeah. Say what you were saying. Camille, >> the only thing that caught me off that was um the realizing was like a linear function thing. Well, not function, but I would but I was able to plot the graph properly with the x and y.
>> I did I did this um this.
>> Okay. Well, I had to say something, right? This is a function, right? This is a function. It's a linear function.
Now, for anybody in class that has a hard time recognizing >> Yeah. So any if anybody has a hard time figuring out what is a a linear function, just look at the rate of change. As time changes, the cost changes by $80 is a fixed rate of change. If it's a fixed rate of change is a line, is a linear graph. Is a linear function. And here I saying again, if the rate of change is the same, so like time and cost changing by the same amount, $80 line line.
I hope all you're okay with that.
So what is my first point?
>> One on your x- axis and one to three on your y axis.
>> Right. Where's my other point? What is my other point?
>> Cool. Cool. Cool. Where's my other point?
>> Three on the X and 290. Anyway, >> okay. So, I think we get the idea. Now let's try to come up with a suitable scale. So ideally a graph should take up one and half the page.
So let's start off with what's on the x-axis. We have to count from 1 to 7.
So we have 16 blocks on the x-axis and we need to go up to seven. Could anybody think of a suitable scale or not? 2 cm represent one unit. I agree. So, one, two, three, four, five, six. Oh, no. Oh, no. No. I don't want to write that. You know, I don't want to write that number after that. Six.
>> Seven.
>> No.
>> You have to say it. You have to.
>> All right. So, 1 2 3 4 5 6 7 8. Cool.
Now, we need to figure out a suitable scale for the y axis. So, we need to go up to 610. That's what we need to We need to go up to 610. So, anybody has any recommendations?
>> So, I use one mini block as 10 70 cm.
So, um two blocks represent 100. That's how I did it on the y axis.
>> I would advise that as well. Two blocks is 100. Now, let me explain why I'm saying that. So, again over here in this particular graph, we have 16 blocks, right? We have 16 blocks and we need to go up to 610.
So a good scale we could use is every two blocks is 100.
Because if I do that, somebody tell me if I do that, how much blocks am I going to occupy there? So I'm saying two big blocks is equal to 100. And we need to go up to 610, which is approximately 600.
How much blocks would I utilize? Does anybody know how much blocks I would utilize?
12.
>> 12. Yeah, 12 is correct. And isn't 12 more than half of 16?
>> Yes. See, >> so we could use that. Cool. So, I'm going to label this 100.
I'm going to label this 200.
I didn't do a live in a long time, boy.
Like a lowkey nervous. A low key. Low key. Yeah. Yeah.
And with all the technical difficulties and the Wi-Fi and thing, I lowkey feeling nervous. So bear with me. The vibes will come in just know the vibes will come in. But I nervous.
>> No worries, sir. Me and Nikolai with you.
>> Okay. Okay. My two sons.
>> We on the stage with you right now.
>> Yeah, boy. Cool.
>> And then Nikol watch.
>> Nikolai. Nikolai.
Yes sir.
>> So here what if there's anybody confused as to the scale I used just tell me and I'll try to explain it.
So if there's anybody confused here in the zoom just tell me.
>> Excuse me.
>> Yeah. Yeah. Talk to my Victoria.
>> Um I kind of confused on how you figure out how to um number the scale. I'm not sure.
>> Okay. No problem. So generally speaking, we should occupy more than half of the graph. So first of all, do you understand that the time is going to go on the x-axis? Let me know if you're with me.
>> Yeah, I understand that part.
>> All right. So we need to go up to seven.
We need to go up to seven.
Now over here on the x-axis, we have 16 big blocks. Seeing that?
>> Yes sir.
>> 16 big blocks. Now I need to occupy more than half of those for half of that 16.
More than half of the 16.
So if I use two blocks is seven, how much blocks would I occupy?
If I use two blocks is seven, how much would I occupy?
What I saying, buddy? Sorry about that.
Yeah, if I say two blocks is one, how much would I occupy?
So I say in two blocks is one and I have 16 blocks and we'll be going out to seven. So I say in every two blocks is one. So like this is one, this is two, this is three, this is four, this is five, this is six, this is seven. How much big blocks did we occupy? Some of it >> is it 12?
>> Nah, not 12. So I want to go up to seven. and are saying every two blocks is one. So every one is two. So if we're going up to seven and each two blocks is one, how much big blocks do you think I used?
You could do it. Take your time.
So we're saying >> nah. Okay. Now we are going to erase the scale and let's try to let's try to understand it. Don't feel shame on there's a learning space.
Everything is fine.
Okay.
Yeah. So, Victoria, how much big blocks do we have on the x- axis?
Okay, I'll help you out. Right, we have 16 big blocks. 16 big blocks. Now, we need to cover at least more than half a 16. So, we need to occupy the x-axis.
Now the smallest value is one and the biggest value is what? What's the biggest value over there?
>> The biggest value is seven.
>> Right? As it is right now, if you use one big block is one, is that going to occupy more than half of the graph?
>> No, it would not.
>> So what other scale do you think I could use? Think about it. Um, >> you could use two.
>> Yeah. So every two are going to be what?
Every two going to be what?
Every two would be one.
>> Yeah, we could say that every two is one. And let's quickly check that out now. So that would be one. This will be two.
This would be three. This would be four.
This would be five. This would be six.
This would be what?
>> Seven.
>> Ah. Did we occupy more than half of the 16 blocks?
>> Yeah.
>> Yeah, we did. So, how you feeling about that?
>> Okay, I understand now.
>> Right. That's our problem.
So let's look at the y- axis now. So on the y- axis again, how much big blocks do we have on the y- axis?
>> You have eight.
>> Well, if you're counting the the big blocks, it's going to be 16, I think. I think. Okay.
>> Yeah. 16, right? 16.
>> And now we need to go up to what? What's the biggest value on the y- axis? The biggest value >> 610.
>> Right. We can approximately round that off to 600, right? 600 and down. 600 and >> Okay.
>> So, okay. We have 16 blocks. Yeah. 16 blocks and we had to go up to 600. Hm.
Okay. Let me think. So, N could break up 600 into divisions of 100. So, like 100, 200, 300, 400, 500, 600.
Yeah.
>> Now, if I use if I say every one block is 100, would I occupy more than half of the the y- axis?
Ah, so 100, 200, 300, 400, 500, 600. Did I occupy more than half the y- axis?
>> No.
>> No. So, what you think is the next move I should I should take? I think I should do.
>> You should try two.
>> Yeah. So every two is 100. So 100 200 300 400 500 600. Doesn't that occupy at least more than half of the y- axis?
>> Yes, I do.
>> Right. So hope you understand that.
Nice. Nice. You good?
>> Yeah, I understand.
>> Okay. Nice. So here what my advice is pick. Okay. Break up the look at the largest value, right? Look at the largest value. See how you could fit it in the graph and then probably expand the scale. So you see how one two three four five six seven. You see how that it fitted right but it was too small. You seeing that it fit but it was too small.
I mean >> so the next thing you could do is potentially go to every two blocks is one. So hope you understand that.
>> Yeah. So here what guys we need to figure out what one of these small blocks is equal to. So first of all how much mini blocks do we have from 0 to 100?
Yes paper two lives after the 7th of May we outside every single day. Every single day we're outside. Seventh time of me seventh of me. I tell you mark down the calendar you know I will I would figure out how to use OBS and sing by then. I might probably upgrade the Wi-Fi. So, make sure you're there seven Tommy. We're going right down to the exam. We're going for like six hours of maths every single day or something. You know, it's a mad man.
Yeah. So, how much small how much of the smallest blocks make from 0 to 100 there? Could somebody tell me that?
How much small blocks making 0 to 100?
10.
So if 10 small blocks I could call that B is equal to 100, what would one small block be equal to?
>> 10 >> 10, >> right? And to do that you would have divided by 10 on both sides. So one block is 10. So in other words, this will be 10. What would this be? 10.
Somebody >> 20 >> maybe 10 20 30 40 >> 60 70 80 90 100 Okay, is there anybody confused as to how I figured out the divisions for the y- axis talk?
>> Okay, happy to hear that. We understand that. And well, we really don't need to figure out the divisions for the x-axis here because if you look at the values we had to plot, it's just 1 2 3 4 5 6 7.
Oh god, why did I do that? That was unintentional.
>> That was unintentional. But um we go now. So the first point is 130. So here when you're plotting points, you're going to go on the x axis and then you're going to go on the y axis. So let me show you what I mean by that. So my first point is 1 comma 130. I'm going to go to one on my x axis. So I'm at one and then I need to move up to 130 on the y- axis following the y- axis. So this is 100 over here and now I'm trying to go up to 130. So how much small blocks would I have to move up to reach 130?
Somebody tell me that >> tree >> three >> right? So this is 100 this is 110. This is 120. This is 130. So my first point would be right here. Is there anybody at all that is confused by that? If you are, don't be scared to tell.
Is there anybody confused by that?
>> No.
>> All right. Um, Romano, Nikolai, put the meeting information in the Tik Tok live.
Yeah. I I can't really do so much thing at the same time. Just share share the thing all over the place. Share the thing all over the place. Yeah. Share the thing all over the place.
Right. Let's do the other point. So who on knew the other point? You know what?
Victoria. Victoria should have known the other point. Yes. So Victoria, my second point is 2, 210. So what's my first step?
Tell my Victoria was my first step if you're trying to plot that point.
Kiana here in Victoria. What about Nikki? Nikki was the first step in trying to plot 2 comma 210 place dead boy X >> where the Wi-Fi >> 210 >> wait the Wi-Fi player. So you're saying to go by two on the x axis, go by two on the x axis. Then what?
>> Then 200 in in the y axis.
>> Right. So tell me when to stop. Right. I go in. I go in. I go in. I go in. I go in. Tell me when to stop.
>> So it would be one block after 200.
>> Yes. Big up yourself, boy. Nikki boy.
Hey, big up yourself. Now we talking about you don't know.
All right. I want somebody else to help me with the points. So, Victoria, I see you had unmuted but my Wi-Fi playing up.
So, see if you could talk now. Try talking now.
>> So, um I'm not sure about the information you get to the side. I don't count it because they make a lot of noise here.
>> Tell them to can't say what I want to say on a live. Hey. Hey.
Anyways. Anyways. Yeah. Victoria what I saying right? You have 10 small blocks from 0 to 100. So 10 small blocks is going to give you 100, right? Let me know if you're with me, Victoria. 10 blocks, right? And you need to figure out what one block would be. So if 10 blocks is equal to 100, you divide both sides by 10 to find for one block.
>> So one block would be 100 over 10.
Where's 100 over 10?
What's 100 over 10?
Okay. I'm not hearing Victoria. Are you hearing me?
>> So, it will be 10.
>> Yeah, it will be 10, right? And every So, every small block, every small increment is 10. So, watch. 10 20 30 40 50 60 70 80 90 100. You with me?
>> Yeah.
>> Okay. Okay. Nice. Big up yourself. So, 3 comma 290. Now, so the first thing you had to do, you had to go to three on the x-axis. Let me know if you're with me there. You had to go to three on the x axis because it's three, >> right? 3 comma 290. So on the x-axis. So now I need to move up to 290. That's what I need to do. So I'm going to go go and I want you to tell me when to stop.
Right? So we at three and I'm going to go go and tell me when to stop. Tell me when I reach 290.
Um, I think you could stop under 300.
>> Big up yourself. Big up your whole self that we talking about, right?
I hope all you see that math really not hard, you know. Math's really not that hard. It's really simple. So, watch. 3, 290. I stop one block below 300 because every small block is 10. So, 300 minus 10 is 290. Okay. Who wants help with the other points? Do we have any other volunteers? at a point. The other point will be 4, 370. Any other volunteers?
Nikolai, you even need to raise your hand, boy. Look who raise their hand.
Nikolai. Yeah, Nikolai winner. Tell me what to do. Tell me what to do.
>> YouTube first access, which is four, right?
>> And then we go all the way to 370.
Someone went to stop right here.
>> Yeah, right here.
happened to YouTube >> right now. My internet is really bad.
That was the problem.
>> My internet is really really bad at the moment.
>> Yeah.
>> Yeah.
>> Yeah. My internet is really bad at the moment. I just put out there. It's kind of bad.
So let's look at the other point. The other point is 5 comma 450.
So I'm going to expedite the process and speed it up a bit. So it's 5a 450. We have to go to five on the x-axis and I'm going to go all the way till 450. So 450 would be right here. All right. This is 450. I hope nobody is confused by that.
So the point is going to be right here.
Okay, somebody tell me fast. What is the next point? What is the next point?
What's your next point?
>> 6530.
>> 6, 530. Big up yourself. So, we're going to go to 6 on the x axis and then we're going to go then we're going to move up to 530.
So, 6 is over here. I going to go go. I want to go up to 530. 530 there will be three small blocks after 500 because again every small block is 10 that's what we know by the way are you seen the line that I was talking about all seen the line I was talking about >> because a line has a constant rate of change right one thing changing with respect to the other one at a at a constant rate that line the last point is 7 610.
This can't be a coincidence how they're playing these numbers away. Can't be a coincidence.
I fed up. See that number, right? 7 610. So, I'm going to go to 7 on the x-axis and I'm going to move up till 610. Okay.
Okay, let me know if there's anybody that's confused as to what I did so far.
Is there anybody confused as to how I plotted those points?
>> Yes, sir.
>> Anybody?
>> Is there anybody in Zoom? Anybody in the Zoom that is confused?
>> Okay. Right.
>> All done seeing vibes, vibes, vibes. If anybody confused, I'm going know. I see Claire raise your hand. Yeah, Claire, talk to me.
I saw Claire raised her hand. Claire, talk to me. Let me know what's going on.
Okay, I'm not hearing Cle anymore.
So, here's what I have all my points.
So, now I could just connect them to make my line.
So what are the chances we might get like something similar to this in paper country? I I can't tell you for sure, right? But this is something they typically bring. It's not the first time they they brought a question like this.
They they had one where people were renting DVDs or CDs. It's the same kind of concept. So this is something that comes frequently. I wouldn't say it's something that that is unusual. It could come.
>> But um the topics that I would recommend you guys going over measurement and geometry, algebra and functions, statistics and data handling, relations, functions and graphs, vectors and matrices, consumer arithmetic and investigations.
Hey, look, Leon Bailey boy, the goat for Guyana. Yeah, big up Leon.
>> Hey, big up you, sir. Big up.
>> Yeah, boy.
So, let me just um take my ruler, line it up with these points, and I'll draw my line. And you guys are going to see something real cool, you know. Watch it.
Mind blown. Watch what watch thing watch thing. When I connect the line, could somebody tell me what the y intercept is? Okay. Wait, wait. If you don't know what the y intercept is, is essentially where the graph cutting the y ais. And remember this was the y- axis. So, at what value does my line cut the y- axis?
50 which is flat inspection rate.
>> I see that we're talking about see the math bad like that. Yeah, boy. Hey.
>> Yeah. Yeah. Yeah. Yeah. Yeah. So, at the start when we looked at that table, we cannot call that, you know, we cannot call that. We saw it.
Um, let me go back to the table to show you what I'm talking about. So, again, the pattern here was for every hour that goes by, you have to you have to pay 80.
Pay 80. Pay 80.
And if you went backwards, so let's just say you take away 80 from 130, you get 50. And you take away one from one, that's zero. So that would have implied that at zero hours the cost is 50. But at zero hours, the man do no work yet.
So that had to be the inspection fee. I hope I understand that. The math's clicking. Let me let me know if the math's making sense.
>> Yes.
>> Cool. And if I were to read off if I were to read off this point, what would that point look like? What would that point look like? Somebody tell me.
>> 050.
>> 050.
>> Hey, big up on yourself. 0 comma 50.
Nice. And remind me, what were we measuring on the x- axis? The x- axis.
What were we measuring?
>> Time.
>> Time. And what were we measuring on the y axis?
>> Cost.
>> Cost.
>> So you can see for yourself, right? When the time is zero, where's the cost?
>> 50. 50.
>> No. If the time is zero, if the time is zero, did the man start working as yet?
If the time is zero, he do anything yet?
>> No.
>> The man the man do nothing yet. He you give him that 50 just for him showing face, right? That is what the 50 is for.
The 50 is the inspection fee because at a time of zero, >> you're paying 50. You're a man.
Wait. Set that back one more time again.
My wife.
>> Set that back one more time.
>> Say again. One.
This Wi-Fi real bad boy. All I hear is one mark on a test paper. That's all I hear.
>> All I hear was one mark on our test paper.
Yeah, good.
>> But why his wife being so fast?
>> Cuz again, one mark on our test paper for just writing.
>> It don't work like that. Romano Romano Romano. It don't work like that. It don't work like that. Just because you're writing, you're not going to get a mark. But I wish it was the case, you know. I wish it was the case. I see Nikolai raises Nikolai.
>> I don't know if this might work, but you might have to take off the YouTube because I don't think it makes sense that static. I think that the that is what messing up the internet as well.
>> All right. So, have anybody on YouTube though?
It had like one person and then it came up.
So how much people have right now in YouTube?
One >> I see.
>> Okay. Well, including me.
>> Wait, boy.
>> I was on.
>> Okay. Well, let me stop the YouTube and but wait, I already already um doing it.
So, I guess it don't make sense because as soon as I finish with this video, automatically upload. So, we'll continue. We will continue. Fingers crossed the Wi-Fi improves over time.
But I definitely had to do some work with the Wi-Fi situation.
Yeah.
All right.
So, let's move on.
So, is everybody okay with part one where we had to sketch the graph?
Yes, sir. Yes, sir.
>> Okay. Nice.
Right. Wait, why?
Why everything dying for a boy? My phone dying.
Bad luck. So, what kind of bad luck is this? Boy is because you said numbers.
That is why >> multiple times.
>> I feel it is very bad.
>> I feel it.
All right. So, I'm going live on my other phone.
Okay, let me continue. So, I trust that everybody is okay with plotting the graph. Nice.
So, now we need to figure out part two.
>> Terrible internet by >> it is read part two for >> Wi-Fi.
Um, >> here try taking over the camera. See if it go fix the problem. See if it will help a bit. Try taking over the cameras.
>> Okay, try talking now.
>> You hear me?
>> I hear you better. I hear you better.
For sure. For sure.
Yeah. So, read the question. Come on.
Can I hear anybody so I can read the question?
>> Yes sir. Yes sir. I can read it. I can read it.
>> All right. The question.
>> The equation of the line represents the model to be used to calculate the cost of a job. Determine the equation of the line in the form y = mx + c. Okay.
Great.
Can everybody see that this is our line or no? How many?
Yes sir.
>> Yes sir.
>> Yes sir. Okay. So, let me put down a couple of ground rules, right? Um, what were we plotting on the y axis? Somebody tell me that. What were we plotting on the y axis?
>> It was cost here. And that was represented by capital c. Now, what is x? What were we plotting on the x axis?
>> Time.
>> Yeah. And time is measured in what?
>> Hours.
>> Great.
and C. We said earlier that C would have represented the what fee? The what fee?
Y intercept.
>> Yeah, it is the Y intercept, but in this case it also it also represents the what?
>> Cost the cost.
>> The inspection fee $50.
>> That's the inspection fee. Cool. Oh, taking off all the camera. Real health.
Be seen. A real help.
And if all you had to say, what do you think M is?
What do you guys think M is?
>> Yeah. M is the gradient. You know >> the 80 >> that Yeah. Yeah. That is the 80. The gradient tells us how Y is changing with respect to X. The gradient is the rate of change. And when you looked at the table, you saw that the time and the cost had a difference. Okay, the rate of change there was 80. So I mean you don't even have to calculate the gradient because you know it's 80 from from the table but we'll calculate it anyways. So this M over here tells you the rate.
Tells you the hourly rate.
That's what it tells you the hourly rate.
So let's model our equation quickly. So instead of writing y, what am I going to write instead? Somebody tell me.
Instead of writing y, what would I write instead?
What will we plotting on the y- axis?
>> Cost.
>> Cost.
>> Yeah, that's going to be cost.
>> Um, what do we know the gradient is?
That was the hourly rate. So, where's the gradient?
>> 80.
>> 80.
>> Yeah. Um, what we going to write instead of x?
>> 50.
>> No, no, no, not 50.
>> Yeah. Yeah. We go. I'll just change this to time, right? Yeah. So, we'll say 80 t and then we have to add on the y intercept. What is the y intercept? What is the 50?
>> 50.
>> Yeah, >> that's 50.
So, does everybody understand this? I mean, I'll calculate the gradient as well, right? But let me know if you understand this.
Yes, sir.
Okay, I'll show you guys how the function works just now, but let's calculate the gradient manually.
>> So, somebody remind somebody.
Um yeah, Camille.
>> Oh, I was gonna tell. Yeah. Um >> so that's how I did it. I used to um two points on the graph to find the gradient.
>> That's not a problem.
>> I did it manually.
>> That's not like it was a function or whatever.
>> It's not a problem.
>> Yeah.
>> Yeah. So just a FYI for any of the Eagle Dye viewers as you can see the the rate of change right is $80 per hour. I'm not sure about seeing that because for as for every hour that goes up 80 is added.
So that's how I was able to figure out that that is the gradient because that's the rate of change. Gradient is just the rate at which something is changing. So that's this is the gradient. That's clearly the gradient. But if you did not notice that well you could find the gradient manually and you would to find the gradient you would need how much points somebody tell me to find the gradient how much points you need two points you need two points to find the gradient so the gradient is given by y2us y1 over what so the gradient is change in y over >> one change in y change in x >> correct so y2 - y1 over x2 - x1 one.
Now, we are allowed to pick any two points that are on the graph. Any points that are on the graph.
So, do you all have any recommendations?
And let me just try to draw this graph a bit better. Give me a moment. Going to draw the graph a bit better.
Yeah. So, I want you guys to pick some points on the graph. What's the easiest point to pick on the graph if you allow to say?
>> One and two.
>> Wait, one and two.
>> Can I use the exact points on the line, you know, or you got it to something else? Isn't that right, sir?
>> Yeah. Yeah. Yeah. Because what if this was um a situation where it was a best fit graph. So, you can't pick the points that that you were given. You need to read off points from the graph. So the easiest point that I am seeing here on the graph is the y intercept. That's a very easy point to pick. I'm not sure if you guys seeing that. This is a very very easy point to work with. So I'm going to use this point. So I'm going to use 0 comma 50. So that's one point I could use 0a 50. And so now we need to pick another point that is on the graph.
So we need to read off a point. Are you guys seeing any nice points that I could easily read off? Let me know >> two um two and 210.
>> Wait, hear what I saying, right? You cannot use the points that were given to you. When you draw a graph, you need to pick points from the graph.
So other than the points that we use, try to use some other points.
Try to read off some other points from the graph.
So five and 490 sir. So say that again.
>> What what about 8 and um 700?
>> Okay. 8 and 700. That wouldn't be quite right because when the time is 8 is not exactly at 700. So that wouldn't be exactly 8a 700.
But you know where it would be?
>> Yeah. Um 8 and six.
>> Um >> 8 and 6 what?
>> Like 690.
>> Yes. 8 and 690. So here what Akira that's a completely valid point but I see some easier points. You know there's there's some easier points there on the graph. There's an easier point on the graph.
>> 2 and a half and 250. So I use seven and 16 and five and 450.
>> Now here what I saying you typically can't use the points that are given to you.
>> You need to draw a graph and then take points from the graph.
>> You need to draw a graph and then take points from the graph.
>> Well that's the two easy points that I saw when I um the >> Wait, it sound like you use >> you use these points that were given.
>> Yeah.
Now when you draw a graph you have to pick points from the graph to do the gradient typically typically.
>> So an easy point that I'm seeing from the graph >> off of this graph here >> easy point that I'm seeing from the graph.
>> So this point would be 2.5 >> So this point would be 2 >> 250.
Let me know if you guys understand that.
2.5 comma 250.
>> Yes sir.
>> Yes sir.
>> So that's an easy point to use. So I could use 0 comma 50 and I could use 2.5 comma 250. So let me work with it.
So here they said it really doesn't matter which one you call the first point or which one you call the second point. Either way is fine, but we need to pick one. So what do you what do you guys want to call the first point?
A and B. We could call it A and B.
>> Yeah, >> you could call the points A and B, but it doesn't matter. Um, we just need to label it. So here, what? We could call this the first point. Again, it doesn't matter. It'll work out anyways. So we could call this one X1 Y1 here. And we could call this one X2 Y2.
Let me know if you guys okay with that.
It really doesn't matter. It doesn't matter. I could have as I'll show you guys. It doesn't matter. I'll switch it around and you'll see you get the same answer. Does not matter.
And let me just clarify this. The points are picking from the graph, it had to be on the line. If it not on the line, then it doesn't obey the function. It needs to be on the line. So, I just pointed that out there. Right? Notice the points I picked were on the line. You need to pick points that are on the line and you can't pick any of your points that were there already. You need to draw a graph and pick points from the graph.
So let's quickly find the gradient. So the gradient here is going to be y2 - y1. y2 is 250. Um y1 is 50 and that's going to be over x2 - x1. So x2 is 2.5.
And what is x1? x1 is zero. So what is 250 - 50? Somebody tell me 250 - 50 is what?
>> 200.
>> Yeah. That's 200.
So 200 over >> 2.5.
Yeah. Where's 200 over 2.5?
>> 80.
>> Yeah. Let me know if you guys get the 80.
>> Yes.
>> Okay, sir.
>> Now, let me prove a point here because some students there is be like so confused when I tell them the order doesn't matter. So, let me just prove that point here because it's important for coordinate geometry. It's really important that you know that the order doesn't matter.
So here what what if I call that x1 y1 and I call this x2 y2 instead?
We're still going to get the same answer. I prom I promise you. So again gradient is y2 - y1 all over x2 - x1.
What is y2? Somebody tell me what is y2?
Where's y2?
>> 50. What's y1?
>> All right. Where's x2?
>> Zero. What is x1.5?
>> So when you work out the top 50 minus 250 that's going to be -200 and 0 - 2.5 that's going to be - 2.5. First of all what is a negative divided by a negative >> positive positive >> a positive that is what a negative divided by a negative is right. So aha we get a positive number. Cool. And well 200 over 2.5 gives us back to 80. Let me know if >> Yes sir. Yes sir.
>> Good.
>> Let me just do a quick recap. When you need to find the gradient for a line, you typically draw a graph. Then you read off points from your graph. Now I doing this because it's very important for physics. Anybody here doing physics?
Let me know. Anybody here do physics?
>> Okay. When I draw a graph for physics, right? enter would have some some points that kind of doesn't fit the the pattern that you notice. It kind of like >> like you go have points like this, right?
And then you have one point out there, >> right? You might have one point off there.
So these might have been caused due to some error in the experiment. So what you need to do is you would first draw a best fit. You draw a best fit and after the best fit then you'd be able to actually take points from your graph. So the I want to apply the same concept here in maths. You draw your line. After you draw the line, read off two points that are on the line. So I drew my line and I and I read off two points that were on the line. I'm not going to use any points that were given to me. I'm going to try to use points from the graph. I'm going to try to read off points from the graph. So that's general rule of thumb. Let me know if you guys understand that. So for a line, you're going to draw a graph. Going to draw a graph. Then you're going to take two points on the line. Has to be on the line and you find the gradient. Are they okay with that? Yes or no?
>> Let me know if you guys okay with that.
>> Yes, sir.
>> Okay, good.
>> Question.
>> If I wanted to find ingredients, could I pick a point here and a point here?
>> Yeah or no? Illegal?
>> No. No.
>> No.
>> What about over here and over here?
Illegal or illegal?
>> Illegal.
>> Right. What about here and here?
Illegal.
>> Yes, sir.
>> Yes. Yes, sir.
>> Because it's on the line. It follows the relationship. Now I want to make something abundantly clear because some of you guys would find this and you would have no idea what this means.
You'll have no idea what that means. I know that how much of you guys here you find this but you have no idea what I mean. Tell me. A lot of students do that and they doesn't know what you mean. So somebody tell me if they're confused. Do you know what this stands for?
>> Yes sir.
>> Okay. Well, I going to assume that they don't understand and I'm going to show you something really cool. This fun, this is a function. You know, there's a function. A function is something that takes in a input. It would do something to the number and give you an output.
So, this function relates what to what?
Somebody tell me what do you think this function relates? It it relates what?
Two things. Nikki, Nikki, see if you could tell me what does this function relate? What two things?
>> So, the inspection fee. No, this one is the hourly rate and the inspection fee.
>> Um, you're not wrong, you know, but I looking for I'm looking for something in terms of the variable. So, like remind me what does the C stand for? What does the C stand for? The C >> cost, >> right? So, it's we have an equation here that is telling us what the cost would be in terms of what? What's the variable there? What's the variable there?
>> Um, this would be X and Y. Now let me take a little step m >> right so here here will okay I'll go over the whole concept right so a line would always be uniform y is equal mx plus c nowiki for our graph what did we have on the y ais we had cost on the x-axis what did we have we had time so instead of writing y I wrote c because Cuz that's what because that is what I had on the y- axis. I had cost you with me.
>> Yes sir.
>> And for the x- axis I had time. So that's why instead of y saw me wrote cost and instead of x you saw me wrote time.
So this function here it tells you how the cost is linked to the what? It tells you how the cost is linked to the >> time.
>> Yes. And you're probably saying, "Sir, I don't believe you." You know, I don't believe you. Let me share some proof.
So, Nikki, from the graph itself, when the time was 2 hours, where's the cost?
So, like, I want you to I want you to zone in on this example here. Here's a little example so you understand what happening. When the time is two, where's the cost?
>> $210.
>> So, Alia, if I use the function I came up with, shouldn't it shouldn't it give me the cost when t is two?
>> Yes, sir.
>> Yes, it should. It should. So from the table we see when the time is two the course is 210. Let's check to see if that's true. So Nikki, we want to verify that when time is two, the cost will be what? What we're trying to verify here?
>> When the time is two, it the cost would be $210.
>> Let's see now. So 80 I'm going to plug in two into the function. So 80 by 2 + 5. Where's 80 by two?
>> 160. Where's 160 + 5? Um 50. Where's 160 plus 50?
>> Just seeing it now. Are you seeing what what this function is doing?
>> Yes.
>> Yeah. It tells us how the cost is linked to the time. So Nikki, where's 160 + 50?
>> So 210, >> right? 210. So was our function faithful to the actual values in the table?
>> Yes sir.
>> Right. Because Nikki from the table when time is two what the cost supposed to be?
>> 210.
>> I want to I want to plug that into the function we came up with. Did it give me back the 210?
>> Yes sir.
>> And this will work for any value of time. granted is like is more than equal to zero right cuz you can't have negative time that nah time is a scalar quantity physics people don't know that you know what I know all has some trust I know all trust is not so let me try it for another one here what >> you want to try it for any other values in the table >> sir try five >> try five and 450 >> yes sir >> so Nikki according to that right when The person would have worked for five hours yet I had to pay them how much money?
>> $450.
>> Let me see if that fun. Let's let me see if we function faithful to that now. So we want to figure out the cost when the time is is where's where was I again? I have the memory of a goldfish. T is equal to 5. So Nikki, what would I put into the function then to find the cost?
So it would be 80 * 5.
>> Yeah. Plus 50. What is 80 by 5 + 50?
Somebody tell me what is 80 by 5 + 50.
What is that?
>> 450.
>> 450.
>> Yeah. Nikki, let me know if you're getting any 450. 80 by 5 is 400. 400 + 50 is 450.
>> Yes, sir.
>> And isn't that what was said in the table?
Yes sir.
>> Right. So does everybody understand that we came up with a function relating the cost to the time? That's what we did.
>> Yes sir.
>> Again if all it come to math vibes the the point of my channel and thing is really to develop a deeper thinking for math. I don't just want it to memorize this learn and get no no we thinking deeper than that. We better than that.
You know I am stronger. I'm better. I don't know what I mean or like I got too old. Oh, you know what I mean?
>> Yeah, I know it.
>> Yeah.
>> Okay, cool. So, I hope everybody okay with this. So, we just came up with a function linking cost to time. So, I want somebody to help me with part three. And we know the answer. Part three, right? What's the answer for part three? The inspection. The inspection cost. What's the inspection cost?
>> $50, right?
So, the inspection cost is $50. And if there was anybody here that didn't understand that, fear not. I'll go it over quickly.
So, inspection cost, somebody talked to me, right? This is common sense. This is pure logic. When we talking about inspection cost, did the person do any work yet? Did the person do any work yet?
>> No. No, sir.
>> No. People on Tik Tok are inspection fee. Did the person do any work yet? If is our inspection fee. Did they do any work yet? Is our inspection fee?
Somebody give a give a give a guess. Is that inspection fee? The person started work yet?
>> Okay. People on TikTok kind of dry. But um the answer is no. Typically you would ask somebody to come over check check the machine or something. They would charge a cost and then they would start to work on it. So in other words, the inspection cost will be the cost you have to pay when the time is what? When the time is what?
>> Zero.
>> Exactly. When the time is zero hours, that's like a fixed fee you had to pay.
Yeah. Are they sure they understand that or no? I feel like they do fully understand that.
>> I understand.
>> Nobody please.
>> I understand.
>> Sarah, you see I like Sarah. Big up yourself, Sarah. I'm happy that you could admit you want me to go over again. That's good. That's a sign of learning. So Sarah inspection if the person comes to do inspection did they start working on it as yet? Did they start working on the machine or something as yet?
>> No.
>> No. So the time would be what? If they didn't start working as yet, what's the time?
>> Zero.
>> Exactly. The time is zero.
And when the time is zero here, what Sara end ID? When the time is zero, you shouldn't have had to pay a fee.
>> No.
>> No. Because he didn't do anything yet, right? But you're seeing here from from the graph that when the time is zero, the cost is 50. You're seeing that, right? When the time is zero, the cost is 50. So, did he do any workers yet?
>> No.
>> But he's still getting money. Yeah.
>> No. Okay.
>> So, what would that have to be then?
Would that have to be then? That had to be representative of what >> that 50 was um think they have to pay. Yes. Yes.
Yes. So that's what he has to pay.
That's the inspection cost. Let me know if you understand that.
>> Yes.
>> One more time. So the inspection cost is the amount that you have to pay regardless of if if you do any workers yet. So he didn't do any workers yet or not. So the time is zero, but you still had to pay some money because he had to inspect. He had to do some inspection first and then he would start to work.
So from the graph, you're looking at the y intercept. When the time is zero, you notice that you still had to pay some money. You had to pay $50 implying that that is the inspection fee. That's the fee you had to pay at the start before he do any work on the device. Well, I don't know what you do again, buddy. I forget what I forget what this man is doing. Plaxton. He owns a plumbing company. Okay. A plumbing company. So, he had to come on and and inspect the plumbing before he do any work. So, that is time zero. He didn't do any workers yet, but you still had to pay that 50 because he had to come and inspect the place. Everybody feel like they understand that or no?
>> Yes, sir.
>> Okay. Bet, bet, bet.
All right. Um, I want somebody to tell me with part B. So, they're saying Plaxton received 490 for our job. How much money he gets?
>> 490.
>> So, so it look Bali dog. Bali look the goat. Big up Bali one time. Yeah. So Plaxon received 490 for a job. So that implies that he would have charged how much? In 490.
>> Yes sir.
>> Yeah. So this would have be the cost of the job would it not?
>> Yes sir.
>> That's the cost. And they want I don't know why the man name is Plaxton. Best could have just put Plankton and done.
Determine the number of hours he spent on this job. So they're giving us the cost and they're asking us to find what?
What are they asking us to find for >> the hours?
>> The hours you spent, >> right? So, they are giving us cost and they're asking us to figure out the time he spent on the job. So, is there a formula we came up with that relates cost to the time?
>> Yes, sir.
>> Yes, sir.
>> Yeah. We know that the cost is equal to 80 by t + 50. So, if I wanted to figure out the time, then I would just have to plug in the what? What have to plug in?
>> The cost.
>> The cost.
>> Nikki, let me know if you're saying that the cost. Wasn't the cost to us?
>> Yes.
>> Yeah. The cost was given to us. So, we are going to say 490 and that's going to be equal to 80 t + 50. Now, when you look at this, what is how much unknowns you seeing there? How much unknowns are you guys seeing?
>> One time, >> right? And you could only solve one equation if it have one unknown. If you have two unknowns, you would need two equations cuz you know simultaneous equations.
>> Yeah, but generally speaking, we want to end up with an equation with how much unknowns? How much unknowns you want?
>> One.
>> One is the ideal thing. And that goes for beyond maths. Yeah. One is enough. I go put context to that. One is enough.
More than one is headache. Not that I have any experience with more than one, but like I just say >> I just say I I only had one. Like I have my girlfriend since for five, six years.
I happy. I happy. You know, one one she looking at this.
>> Yeah. Yeah. Yeah. I I've never known anything but one. One is enough. Two.
>> I had my cap calculator since primary school. Just saying.
>> Okay. Boy, you have one real son and one adopted son.
>> Yeah, boy. All all the T people on Tik Tok, right? So you see this man Romano.
That's my son, right? Wait, no. I saying Romano is my adopted son. He's my adopted son. But my real son is really Nikolai. You know my real son is Nikolai. Yeah, that is the lord to behind math vibes. That's our little law if you didn't if you didn't know. So let's solve for t. So we have 490 is equal to 80 t + 50. They're trying to find for t. So we need to isolate t.
When you look at the right hand side, is t the only thing there?
No sir. No.
>> No. Now here what a mistake some students would make is they would try to minus 80 and all kind of thing. Noah, you can't do that. You cannot do that.
You cannot minus 80 because the 80 is telling you how much is telling you where you're multiplying time by. So 80 by t 80 by t. You can't minus 80. You could probably divide by 80, but you can't minus 80. You could only do the opposite operation. Right? So we see now we have a 50 on the right hand side. So we need to get rid of that 50. So how could I get rid of that 50? Somebody tell me 490.
>> Yeah, I'd move it across. Now a way to think about it as well is I could take away 50 on both sides because 50 minus 50 that would eliminate it. So think of it like this. You move it across change the sign or you do the opposite operation on both sides. So you take away 50 on both sides or you move it across and change the sign. Both is fine. So you're going to end up with 490. 490 minus 50. And that's going to be equal to what?
>> 440.
>> That going to be 80t.
>> What is 490us 50?
>> 440.
>> Ah. So we have 440 is equal to 80 t. So we have a t being multiplied by t. And we're trying to find for t. So where's the opposite of multiplying by 80?
>> Right? So we need to divide both sides by 80 if we want to get rid of it. Ah so you see the 80 and 80 cancel off. So now we could find for t. So somebody tell me what would t be equal to? What would >> 5.5 hours?
>> 5.5.
>> Nice. 5.5 hours.
Everybody okay with that?
>> Yes sir.
>> Yes sir.
>> Okay. Now I'm going to say it in big.
That was not the only way you could work that question. They could have also used graph and this is prime time to blow all their minds.
So if we were to use the graph right the first thing we're seeing is the course is 490. We're seeing that. So I'm going to go to my graph and I'm going to go on the y axis. So 490. Where is 490? Could everybody agree that 490 is over here?
>> Yes sir.
>> Yes sir.
Let me know if you're seeing that that's 490 over there. Yeah. No, maybe potentially.
>> Yes, sir.
>> All right. And then Okay. So, you see the 490 it cuts the graph at this point.
So, then you take a a vertical read off to see what the the time would have been.
What does the time look like it is?
Somebody tell me.
>> 5.5.
>> That is why he's saying honestly, you know, the maths mats.
>> Yes. So I just check prob probability like that.
>> Probability like that.
After class you tell me what you mean by that.
I might be concerned or I might be impressed. But you got to tell me what you mean by that.
>> Might be concerned is crazy.
>> I might be concerned or I might be impressed. We don't know. But um let me wrap up everything now. So over here we have a graphical representation where you could represent this on pen and paper with this with this equation we came up with with this function right. So you see that that that that C is equal to 80 t + 50 that encompasses the whole graph with just this one line.
So a function tells you the graph in like one line. So probably understand that it's pretty cool right? So you see when I plugged in 490 into the function, so I plug in 490 for C and I made T the subject of the formula, I got T to be 5.5 O. That's why I got T to be. And when I read it off from the graph, so I went at 490, I took our read off, I also got 5.5. So that was really cool. And here what if you are having trust issues? Let me show you what you could do. Right? So in maths, where's our equation? Somebody tell me fast. What is an equation? What is an equation? What does that mean? An equation?
>> Something equal to >> one side had to be equal to the what?
>> A number.
>> Not.
>> So like in maths an equation just simply means the left hand side had to be equal to the right hand side. That is what it means. Now in the question, what did they tell us the cost was? What was the cost? 490 >> 90.
>> Okay. And what do we find time to be?
>> 5.5.
>> So if I plug it if I plug it back in into the function, >> what suppose again I multiply this out.
What suppose again?
>> The same thing on the left hand side which is 450.
>> 490. If we correct, if we are correct.
>> So what is 80 by 5.5?
Somebody tell me 80 by 5.5. What's that?
80.5 440 440 40. Oh, hey. What is 440 + 50?
What is 440 + 50?
>> 49, >> right? So you see, makes sense, right?
>> Yes, sir. So most things in maths could be checked back by simply plugging it back in into the equation because in maths you're trying to solve for the the variable or the unknown that would give you that would make the equation satisfied. So left hand side equal to right hand side are you okay or not?
>> Yes sir.
>> Yes sir.
>> And this is some proof.
Okay. So this is the calculation method.
This is the calculation method. And well, obviously you had the graph here.
This is the graph method. The graph method.
Boom.
So after we're done with the paper, we we'll run through the whole thing just to make sure everybody's fully like on the same level. Like something about me, if you go on my YouTube, the videos will be long for a reason because I I I have like OCD. I cannot move on if I know a student is confused. Everybody had to understand otherwise we can't move on.
Right? Everybody had to understand. Uh check our pH bets. Ah, so is everybody okay with the first question with how we plot the graph, how we found the equation, how we got the inspection cost and how we figured out the the time if you okay with this.
>> Yes, sir.
>> Okay, good.
Right. So, somebody get us a read from her. Give us a read.
Why the man name Blackton?
>> I don't know. Yeah. Yeah. But somebody give it a read. We wasting time.
Somebody lock in. Lock in.
>> And wait.
>> Now working.
>> Well, every time I ask to read that question, I know I know it taking a little while. This is how I just feel on the inside. Like literally, I feel like this on the inside. It's kind of nerve-wracking. I don't know if anybody going to answer, but yeah. Yeah.
Continue, Sarah. Yeah.
>> I said if no one was going to do it, I would have read it.
>> Yeah. Well, Nikolai is my son. Of course, you going answer. Of course. Of course you going answer, right? But yes, s go.
>> L and are now working jointly and they must settle on a common model to be used to calculate the cost of a job. Lat charges $50 for inspections and $90 per hour to do a job. But unlike Plaxton, she refunds the inspection cost to the customer once the job is given to her.
Plaxton wants to compare the two models.
Using some pair of axes on page five of the answer booklet, draw the line representing the last model, assuming that she is given all the jobs that she inspects.
>> Way boy Sarah, that look like a like a English problem. how long it is, you know, like >> pages look like a paragraph to people.
>> Okay. Okay. Let me show you something, right? In a higher levels. Okay. Let me show you something, right? Let me show you something. You see that paragraph?
That paragraph looking like a whole essay for me, right? Because like when you're doing higher level maths, this is the question. That's the question.
There's no there's no talk about numbers answering. There's no talk about numbers and thing. I mean letters like you see how is that whole paragraph in higher level maths it will be like that like yeah. So >> I hope you're right. I really do.
>> I said that again.
>> I hope you're right because I do hate soon too. So I hope I don't see these word problems come up for me again.
>> You'll see it less. It's a lesser degree but you'll still see it. You'll still see it. But it's a lesser degree. Don't worry.
Excuse me sir. This question has been paper in paper two for CXE. Yeah. What?
Right. I want I want everybody on Tik Tok and YouTube. Everybody watching right here. Maths is maths. Maths is maths. Everything we doing in paper tree could come in paper two vice versa.
Everything is maths. Everything is maths. Math is maths. So we're learning here is application of coordinate geometry right now. That's what we're learning right now. This is coordinate geometry and lines, functions and graphs.
This is application.
So yeah, things like this will come on paper too.
So we actually understand the question, right, Sara? So we have a new person here, right? Leela. Now Leela has a different way of working. She would charge $50 for the inspection, right? And she has an hourly rate of $90 per hour. So Sara, who has a higher hourly rate? Who has a higher hourly rate? Was it here what it um one of you guys send the meeting information on the Tik Tok so people could join the Tik Tok? I mean what I saying people could join the Zoom.
>> Somebody send the information on the Zoom, >> right? So the people on Zoom could join.
I mean, oh my god. So the people could Tik Tok could join.
People on Tik Tok. One of my students go and send the link for the Zoom. Mario go join it. Right now YouTube very unreliable.
So Sarah, who has a higher hourly rate?
Is it Leela or is it Plton?
>> Leela.
>> Yeah, she has a higher hourly rate. But there's a catch. There's a catch. Unlike Plaxton, what does she do?
>> She instruction cost to the customer once the job is given to us. So they don't have to pay unlike if they have plaquin, they would still have to pay.
>> Correct. So once once you so like she would charge you inspection fee right but if you accept the job you don't have to pay it all you understand that let me know if you understand that >> people in the class does everybody understand that if if you if you ask her to do her job right she'll inspect she'll do some inspection if you tell she you don't want the job done you had to pay 90 but if you tell she you want the job done you would not have to pay the inspection fee I'm sorry I say 90 you wouldn't have to pay the 50 for inspection.
I'll run it back one more time. So Nikki, they're saying Leela charges 50 for an inspection and $90 per hour. But if you if you ask she to do the job, she will refund you the inspection cost. So Nikki, if you if you're rolling with Leela, right, if you're rolling with Leela, do you have to pay an inspection fee if you accept the job?
>> Yes, you do. You have to pay an inspection fee, but He gave us >> and afterwards she >> Yeah. Afterwards. Afterwards. So once you accept the job, once you give her the job, she won't charge an inspection fee. She'll give you back the money.
She'll give you back the money.
>> Okay.
>> So let me explain. Right. Let me just say that this is you over here, right?
Wait.
And well, this is Leela over here.
and you say, "Hey, I have work for you."
And she's like, "Bet." Right? She tell you the inspection. The inspection will cost 50 and I have a hourly rate. Hourly rate of 90, right?
So Nikki, let we just say you call she, right? You call she you call she, right?
Um, you have this pipe to fix.
So you call she, right? Right, Nikki?
And you say, >> and you tell she and you tell she to inspect the pipe for you. She say, "Okay, no problem." You know that inspection fee go be it go be 50 >> and after she inspect it after she inspect it you say nah nah I don't I don't wear to fix it you say nah >> what would that mean >> you still have to pay the >> exactly if it tells you >> say yes I was going to say >> well if it tell her well to go ahead and fix it you would have to pay the 90 plus 66 D50.
>> Nah, if if you tell her to fix it, if if you give her the job, she's going to refund you the inspection fee. So, you'll just have to pay the 94 per hour.
That's that's what they're saying over here. Unlike Blackton, she refunds the inspection fee to the customer once once the job is given to her. So, if you if you give her the job, she'll give you back the 50.
But if you just tell her no, you have to pay the inspection fee.
You understand?
>> Okay. I feel like you don't understand now. Let me let it back again.
>> No, see, I understand it. I understand it now.
>> All right. So, Nikki, let me just say you was dealer, right? I say, "All right, Nikki, I have a job for you.
Come, come, come inspect the pipe here."
How much you going to charge, man?
$50.
>> I said I said Nikki, no. I don't like your vibes. I don't like your vibes. I know. I know. I ain't going to fix the pipe. I'll call somebody else. How much I'll pay you.
>> Still $50.
>> Still 50 because I didn't I didn't let you do the job.
>> I didn't let you do the job, right?
>> Yeah.
>> But if I say, "Nikki, I like your vibes.
I like where you're moving. You know, you look like you know your thing. Come do the job." What happened there?
you would have to pay $90 because you the $50 would be refunded.
>> Exactly. So the >> So it would be $90, >> right? So every every hour that goes by, you'd have to pay her 90, but but she would give you back the $50. Sarah Sarah, do you understand that? Sarah, let me know if you understand that. Let me know if you understand.
Yes, sir.
>> So, I'm going to go over her one more time for anybody that potentially might be confused.
So, if you tell her to do the job, you go all you had to do is just pay $90 per hour and she'll give you back the 50.
But if you if you call her and you tell her to inspect a pipe and you don't give her the job, you still you had to pay the 50 and you had to pay the 50. But if you if you give her the job, you don't have to pay her the 50. She's going to give you it back and you'll just have to charge her for the hour.
Everybody here, do you all understand?
Are you sure you understand?
>> Yeah.
>> Okay, good.
So, using the same pair of axes um on page five, draw the line representing Leela's model. Um and this is very important. Assuming that she is given all the jobs that she inspects.
So, Sara, this is very important. It says assuming that she's given all the jobs that she inspects. If she's given all the jobs, you just had to pay $90 per hour, right?
Let me know if you understand that.
>> Yes, sir.
>> All right. So, let's come up with an equation to represent to represent her model. So, the cost would be equal to to what? See, I can figure it out. Now, she she getting all the jobs, you know. So, you don't have to pay inspection fee.
So, what would the formula Lincoln cost and time to be what would it be?
>> That is it. That is it.
>> Plus, >> no. No. No plus. No plus. No. No.
>> Could somebody tell me why I'm not going to add on the um inspection fee? Could somebody tell me why I would not?
>> Because it is refunded.
>> Wait, I hear multiple people. Um, Nikki, try tell me why you said again.
>> Because it is refunded.
>> Why it's refunded though? Why refunded?
>> Because the $50 is >> because she took the job. Once she took the job, the $50 would be refunded.
>> That is what I want to hear.
section fee, >> right? That is what I want to hear. If you guys read this, you'll see that assuming that she's given all the jobs.
So, Victoria, do you understand that once she's given her job, you essentially don't have to pay inspection fee, just the hourly rate?
Victoria, let me know if you understand that.
Um, are you hearing more? No. No. No.
>> Okay. So, let's explain this function quickly. So, Nikolai, do you understand that for every hour that you work for for every hour that she works, you'll have to pay you'll have to pay $90? Yes or no? Cuz that's the hourly rate.
>> Yes. Yes, sir. Okay. So, if she worked one hour, how much would you have to pay her? Somebody tell me. According to the question, how much you'd have to pay her?
>> $90.
>> $90.
>> If she worked for two hours, how much would you have to pay her?
>> If she worked three hours, how much you'd have to pay her?
270.
>> So does everybody understand how I came up with this function over here saying that the cost will be 90 times the time?
>> Yes sir.
>> Okay. So we need to plot our graph now.
>> Yes.
>> So again what we plotting now on the graph we were plotting cost versus time.
So cost versus time. So the cost was the y-axis and the time was the x- axis. So according to her according to her rates, right?
According to her rates, let's come up with a couple points because to draw a graph, we need some points. So when the time is 1 hour, remind where's the cost?
Where's the cost? When the time is 1 hour.
>> Thank you.
How many times >> if she work for two hours, how much had to pay her?
>> Right. Um, how much points you need to draw a line? Somebody tell me how much points do you need to draw a line?
>> Two.
>> Two. You only need two points. So, you don't have to do anything again. You only need two points. But let's just do three to be on the safe side. If she works for 3 hours, how much would you have to pay her?
>> 270, >> right?
>> 270.
>> Let's write this as some as points, right? So the first point would be one comma what? What the first point be?
>> Yeah. One comma 90. What would the other point be?
>> Hey, big up the dog Keen. Big up Keen Ser Mats. Go check him out. He real good too. He real good too. I recommend him.
Yeah. So 190 to 180. And what would the other point be? The other point, >> right? 3A 270. So I really really hope nobody is lost. Again, if you're confused, they said assuming that she is given all jobs that she inspects. If Leela is given a job, she's not going to charge you for the inspection fee. She's just going to get she's just going to charge you per hour. And her hourly rate is 90. So that is why I said if she worked 1 hour, you'd have to pay her 90.
If she worked 2 hours, you'd have to pay her 180. If she worked 3 hours, you had to pay her 270. So her model could be represented by C is equal to 90T if she gets the job. Does everybody understand?
how much time we how do we know how much time to work for though?
>> Um, you don't, but we are creating a a a graph to kind of to see the cost at any given time.
That's all we trying to do. So, >> oh, okay.
>> Because Victoria, we don't know how much time she working for, you know, but if we could come up with a straight line or a function, we could figure out what the cost would be at any given time. I'm not sure if you understand what I mean, but so let me show you.
>> Oh, yeah. Yeah, I understand.
>> If if if we know she getting $90 per hour, right? If she worked for five hours, how would the cost be?
>> What do you have to pay her?
>> It would be >> 90 by >> Exactly. 90 by 5. 90 by 5 and 90 by 5 is 450. So Victoria, we don't know how much time she working for you and all, but we are just coming up with a line or or a function that models um her rates and how you pay her. Let me know if you understand.
>> Okay, you understand?
>> Now again, Victoria, we know that this is also going to be a line because it's a fixed hourly rate. Once it's a fixed change, it is a line. It will look like a line. It be a line. So to draw a line, you just need two points. In part one, they asked us to draw the line representing Leela's model. So what did I do? I came up with some points. So when time is one, you had to pay her 90.
When time is two, you had to pay her 180. When time is three, you had to pay her 270. Really, you only need two points because if you have two points, you could connect them to draw a line.
However, I ch I choose three points just for safekeeping, right?
So let's go on the graph and plot these points.
Uh let's do that.
And again, if anybody is confused or they don't know how it is moved, I will not move on if you're confused. So just ask me. I really don't want anybody to be confused.
Let's put on the first point. So I'm going to use a different color to represent Leela's model. So that going to be 1 comma 90. So 1 comma 90. So, Victoria, if it's 1 comma 90, I'm going to go one unit on the x axis and then I'm going to move 90 up because it's 1 comma 90. Remember, every small small block is 10 units. So, one block less than 100 would be 90. So, let me run it through one more time. You're going to move one to your right. Then, they're going to move up till they reach 90.
So, my point is going to be over here.
Talk to me now. Do you understand that?
Do you understand that, Victoria?
100. Yeah.
>> Right. And then we have 2, 180. So 2, 180. We're going to go by two and then we're going to move up till we reach 180. So 180 would be over here.
Okay.
Right. Then we have 3, 270.
Right? 3 comma 270.
So that would be right here.
Okay. So guys, if we have three points, could you take a ruler and align it and draw a line? Yes or no? If you have those three points, >> yes.
>> Yes.
Are they confused or they understand?
If you if yall if you're confused, right? So, Cassidy, how much points do you really need to plot to draw a line?
Tell me, Cassidy, how much points do you really need to draw a line? How much points you need to see to draw a line?
>> Two.
>> You just need two points. We do three just to be safe, right?
>> So, here what I'm going to do, I'm going to take my ruler. I'm going to line it up here. Um, and I'm going to draw my line.
And a all should already be thinking about points of intersection. Anytime you draw two graphs, points of intersection should come to mind one time. One time H.
Right.
Let me know if you're with me. So I draw a line there. Are you okay with it?
Let me know if you guys okay to that.
>> All right. Nice. Now, something I want to point out.
When you when I drew this line, notice that it cut at zero. It cut the y- axis at zero. Could anybody explain why that makes sense? Could anybody explain why that makes sense? Why does it make sense if it cuts the Why does it make sense that that it cuts the graph at zero? Why does that make sense? Somebody tell me.
Could anybody tell me? It has to do with the inspection fee.
>> So, so because the infection fee So because the inspection fee is zero, it is refunded.
>> Ex Nikki Nikki give a high five there boy. Big up yourself. In the question, they said that when she gets the job, you don't have to pay the inspection fee. So that's why when I draw the graph, you're seeing that the inspection fee going to be zero cuz she gain a job, you know, so you don't have to pay high inspection fee. I really really hope we understand. I really hope you understand. Yeah.
Cool.
So I would have just answered um this question. So using the same pair of axes, draw the line representing Leela's model. Does everybody understand how I did that? Yes or no?
>> Yes. Yes, sir.
Okay, that's good to hear. Right, part two. Determine how long a job that returns the same cost for both Plaxton's model and Leela's model would take.
>> Model and Leela's model.
>> Excuse me, sir.
>> Yeah, Camille.
>> Can you scroll up a bit, please?
>> No problem.
>> You could just scroll up a bit.
Um where C is equal to 90 that part sorry >> over here.
>> Over here itself you know question.
Yeah.
>> Excuse me sir.
is >> wait let me just address let me just address address Camille quickly. So, Camille, you want me to go over the C is equal to 90 part? 90T part.
>> I can wait. My internet kind of bad and there's a slight delay. So, wait.
Danielle Camille, what do you want me to go over?
Sir um like I don't understand why I joined late. Sorry.
>> Okay, no problem. I'll explain that just now. But Camille, I want to know what what is confusing Camille. Camille, let me know what's what's going on.
Well, it was clarify but it wasn't confusing or anything. I just didn't understand the question properly or answer more.
>> I understand the question wanted us so they gave us information for another person Leela and she has a different way of charging people. So they wanted us to plot a graph of Leela's model like how she charges people and that's what we did. And to do that we came up with some points. Now if if you give her the job you don't have to pay an inspection fee.
All you have to do is pay $90 per hour.
So like if you give her the job well if 1 hour pass you had to pay her 90. If 2 hours pass you had to pay her 180. If 3 hours pass you had to pay her 270. And that could be modeled by this relationship over here where t is time.
So, so like as you could see if if she works for 1 hour 90 by 1 is 90. If she works for 3 hours, 90 by 3 is 270. So, k let me know if you understand.
So, that's how I came up with the relationship and I would have came up >> I would have figured out some points and I would have plot it on the graph because they wanted us to plot Leela's model. So the blue line is Leela's model.
Yeah.
Right. So Danielle, let me run through the thing one more time. So Danielle have have another person that was introduced. Leela was introduced and Leela charges differently from Plaxton.
So Plaxton would charge you um inspection fee and then every hour every hour he works you had to pay him you had to pay him hourly.
Leela, however, she would charge her inspection fee, right? But if you give her the job, she'll give you back the inspection fee and you'll just have to pay her $90 per hour. Now, in the question, they wanted us to draw a line to represent Leela's model. So, Danielle, if you give Leela the job, you just have to pay her $90 per hour. So if we want to plot the graph representing her model, we need to figure out some data points, two at least. So let let me explain, right? So Danielle, if if she works for one hour, you pay her 90 because that's her hourly rate. If she works for two hours, you got to pay her 180 because two hours would have went by and every hour she gain $90. If 3 hours goes by, you got to pay her $270. You understand, Daniel?
>> Yes, sir.
Yeah. Sure.
>> Yes.
>> So, Danielle, if if you don't give her the job, what do you have to pay her?
If you don't give her the job, how much you have to pay her?
Wait, I tell her. Tell her. I hear you.
Tell her.
Hey, what is this Wi-Fi?
This Wi-Fi stressing all >> Well, I we I have to add 50 to it to the $9.
>> Is that wrong? Wait, Daniel, if you don't give her the job, you'll have to pay her for inspection regardless. So, you'll have to pay her 50. But Daniel, what I'm saying is if you do give her the job, if you do give her the job, all you will have to do is just pay her $90 for every hour that goes by, she'll give you back the 50 for inspection.
>> Okay. Sure.
>> So, Danielle, if you don't give her a job, but she still inspects the the plumbing, how much you have to pay her?
If I don't give her jobs, so that means I would have to pay for inspection.
>> Yes. Yes. So you'd have to pay over 50.
You'd have to pay her $50, right?
However, if you did give her the job, how much you'd have to pay for the first hour?
>> $90.
Would you have to pay for the inspection?
>> No sir, should give you back.
>> Good. Happy that I understand that. So, we'd have used our information to come up with some points and I would have plot the points on the graph and get Yeah. and get through there. Let me just erase these um red coordinates. I would have put this here so that nobody would have been confused when you were doing the original graph. Yeah, just erase it.
Okay, now we have another question. Determine how long a job that returns the same cost for both Plaxton's model and Leela's model would take. So, we want to figure out the same cost. Same cost.
Same cost. So, if if you see same cost and you're looking for what between the two graphs, you're looking for what?
The same cost.
Um, you guys hearing me? Yeah. Or no?
>> Intersection.
Wait till I'm try changing my Wi-Fi.
Give a second.
Okay, you guys you guys hearing me?
Let me know if you guys hearing me.
Sound check 11 one. Rejie to students.
Are you all hearing me?
>> Yes sir, sir.
>> Okay, I hear a little better now. Um, so if they wanted us to figure out how long a job would take to return the same cost for both Plaxton's model and Leela's model, so we're looking for on the graph. We're looking for on the graph >> where the two lines cross each other.
>> Yeah. Yeah. That's what we're looking for. Now, it kind of hard to read from this kind of from this graph. kind of hard to read, but like if you ask me, I would probably say like like um again, it really kind of hard to say, but it looking like it'd be over here, but that might be hard to read off. Now, here they said, this graph that I did here, it's kind of like a guess. Now, in all the copies I was finding online, I was not finding the graph that CXE would have given the students. So, I kind of come up with this graph here. It' be the same concept in the exam, but I just pointed that out. So maybe in the graph you had a different scale that would have allowed you to easily find a point of intersection. Now over here it's kind of hard to see. So we'll have to plug in and see if it's correct. You'll see what I mean by that.
So um you're thinking well we could probably try >> five.
>> You want to try five? Now the darker will work.
>> So you use the same point the 490 where the green arrows passing through and look like where where that look like where the two lines pass through each other >> it looking so but I'm not sure. Let's verify it. Let's verify it. We'll verify it. So let me show you guys how you could verify that.
So let me explain quickly.
So let's just recall what um Plaxton model was. This was Plaxton's model.
This was Plaxton's model.
And let me show you what Leela's model was.
Leela's model was C is equal to 90T.
It will make so much sense in the end, but stay with me.
We had 495.5.
So in other words, when you work 409, I saying if you work 5.5 hours, if you work 5.5 hours, how much you'd have to pay?
>> $49.
>> Now, if this is the correct answer, it is going to satisfy both equations.
Let's see. Well, we know it going to satisfy Plaxton's model, and we can verify that quickly. So the cost is 490.
And so that's going to be 490 is equal to 80 by 5.5 that's the time plus 50.
Somebody plug that into your calculator and verify that again back 490. Yes sir.
Okay cool. And here what if it is okay if it satisfies Leela's model then this is definitely the answer. So the cost is 490 and what is the time?
Okay. Um, where's 90 by 5.5?
>> 95. So, >> so that's not the exact answer. No, that's not the exact answer.
>> No.
>> And instead of using 5.5 hours, what about if we use 5 hours instead?
>> No, that would definitely not work. That wouldn't work because it doesn't intersect.
Doesn't intersect. Oh, >> yeah. We're looking for a point of intersection. So, here what I'm going to do, I'm going to solve it using simultaneous equations as opposed to this graphical method because it's kind of hard to read from the graph. So, let me show you guys how you would handle that.
So, again, it's kind of hard to see what is the point of intersection from the graph because of how the scale is situated. So, I'm going to do simultaneous equations quickly. For those of you guys that did not know, anytime you want to find the point of intersection, you could solve two equations simultaneously. How much of you guys knew that?
>> Okay. Well, let me just use that quickly over here and see where's the exact answer because that um 5.5 490 didn't work and it kind of hard to read from the graph.
All right.
Okay. What method I want to use Nikolai?
If we doing this using um simultaneous equations, what method you want to use?
Substitution or >> substitution?
>> No problem. So if we are using substitution, we need to come up with our third equation. So we could call this the first equation and we could call this the second equation.
Um when you're doing substitution, you need to write one unknown in terms of the other one. So you could plug it in so you end up with one unknown. So tell me something right Nikolai. Do we even need to find that third equation for this question? Do we even need to do that?
>> No.
>> No, we know how to do that. We know how to do that. And both of them equal to C.
>> Yes, sir.
>> So if both of them equal to C. Oh, this this this looking complicated, right?
But here what I saying both of them are equal to C. So they're technically equal to each other. I could put them equal to each other. So, Nikolai, I could say 90 t is equal to what?
>> Uh, 80 t + 50.
>> Okay, it looking like five was the answer, but you can't really see that from the graph.
>> I'll try to draw back I'll try to draw back the graph a bit neater and we'll see. But five looks like is the answer.
So five is the answer because 80 by five is 400 and the $50 inspection fee that is for Blackstone and for Leela is 90 by five is $450.
>> Cool. So you get the same amount, right?
Yeah. Yeah. Nice.
>> Yeah. So, I'll try to draw back the graph a bit better. But when you work this out, you're seeing that t is equal to 50 / 10, >> right? And what is 50 over 10? Somebody tell me that. What's 50 over 10?
>> Five.
>> Five.
>> Five. And so when t is equal to five, it's supposed to give us the same cost.
And if you're doubtful, you could plug that back into both of the equations. So c is equal to 90t.
T is five. So C would be equal to 90 by 5. What's 90 by 5?
>> 450.
>> Wait.
Yeah. 90 by 5 is 450. All right. That is Leila's model. Let's check um Plaxton's model.
So C would be equal to 80 by 5 + 50.
What is 80 by 5?
450.
>> Well, 80 by 5 is 400 and plus 50.
>> Yeah. Yeah. So, that's your answer.
That's your answer. T is five.
Yeah. Let me let me try to draw my graph a bit better so you can actually read it off from the graph. Don't worry, I'll explain this method just now. But let me try to draw my graph a bit better.
H I could draw this graph better. That's the question.
Let me see if I could draw the graph like 100% perfect.
Uh um does it do any of you guys know about gogging?
>> All right. If I plot the graph in gog, it's supposed to be perfect.
>> Sir, did you say gobra?
>> Yeah, gobbra.
Okay. Do you know about GG bra? Nikolai?
>> I don't think I've heard about it. No.
>> No. But Nikolai, you know about GG, bro.
I I would assure you um how to use GG bra in class. I just always use it to um show a little demonstrations.
Ah, look at look at look at look over there. I'm not sure if you're seeing it.
>> Yes, I can see it. It does look like it passes 35.
>> Yeah.
So I fixed the graph. You really have to be careful how you draw your graph. So let's look at the question again and make sure everybody understands it. So Vid read part two for me.
All right. I see Vid joining here. Vid don't be shy thing. This is vibes. You could talk.
Okay. Can I hear him vid? Okay. I see.
Part two for now.
>> Um, determine how long a job that returns the same cost for both of Pakistan's model and model would take, >> right? So, we're talking about the same cost, right? Vid the same cost. So, here they said Vish Leela doing a job and Flaxton doing a job. Both of them doing a job at at a different rates and different fees. Understand?
>> Yes, sir. But we trying to figure out how much time would have to pass by for both of them to get the same amount of money because then you see the same cost. If it's the same cost, then both of them would have earned the same amount of money. So what does that mean when you look at it on the graph? Well, this this this is about intersection.
This is intersection.
This is intersection.
And you'll see why I saying that. So again, Vish, we are trying to figure out where both of them have the same cost, right? They're getting the same amount of money. The same amount of money.
Understand? The same amount of money.
You with me?
>> Yes, sir.
>> And you understand that two of these people working for different rates?
>> Yes, sir.
>> Good.
So, the red line represents Plaxton. So, the red line represents Plton's model.
This is Plton. Don't ask me why the man don't ask me why the man name is Plton.
I don't know. I lowkey feel like a guy.
I feel like that's a guy in his name. I don't know. Let me let me not say anything controversial. Yeah. Vish. And the blue line represents Leela's model.
Now, are you seeing these lines intersect anywhere? Are you seeing these lines intersect anywhere? Tell me.
>> Yes, sir.
>> Where they intersecting?
>> By 450.
So you have to tell me the x value first. So the x value will be five. And that would correspond to what? If it's on the x-axis, we're measuring what on the x axis? What are we measuring on the x axis?
>> Five.
>> We're measuring what?
Time. I'm not sure if you say time, but time is what we measuring. Mhm. And on the y axis, what we measuring?
What are we measuring on the y axis?
Check the y axis. What are we measuring on the y axis? Cost. So, can you see that when the time is 5 hours and both of them both of them watch money both of them getting >> 1250?
>> You understand the question?
Let me know if you understand that.
>> Yeah. Kind of.
>> Kind of. Okay. We can't work with kinder. We have to fully understand it.
So, Vides, they want us to figure out how long a job would take for it to return the same cost for both Plaxton's model and Leela. If we converted that mojo to English, I basically asking you Vish how long both of them had to work for to get the same amount of money.
That's why asking you understand.
>> Yeah. So, how long would would they have to work for to get the same amount of money?
You understand that?
>> How long would you have to work for to get the same amount of money?
>> So, when you read the graph, how long would they have to wait for to get the same amount of money?
>> Five hours.
>> Five hours. Because at 5 hours, what both of them getting? Both of them getting what?
>> 450.
>> You understanding now?
>> Yeah. Yes, sir. And if you still had trust issues, let me show you something faster. When the time is five and you plug it into Leela's model, this is Leela's model. C is equal to 19T, you're getting 450. When you plug it into Plaxton's model, we're getting >> 450.
>> Exactly. So, Vish, if both of them work 5 hours, both of them getting how much money?
>> 450.
>> You understand?
>> Yes, sir.
>> Good. So this question had to do with intersection. Now graphically you could look for the point of intersection. The point of intersection on the graph is 5A 450.
Is everybody okay with that? Yes or no?
>> No. If you if you didn't want to solve it using the intersection on the graph because you know kind of unreliable, you could have done it using simultaneous equations. So somebody remind me anytime you solve two equations simultaneously what are you finding for graphically?
What are you finding for graphically?
Anytime you solve simultaneously you're finding for the what? Between two graphs. What you finding for >> intersection >> intersection >> right? I can't stress that enough.
Anytime they ask anytime they ask you what value would satisfy both equations or both lines or both Really anytime you see the word both just think about intersection right both.
So anytime you see the word both and you have two lines think intersection. Now let me just show you something to seal the deal. So who here know about geogra again? Who know about it?
>> Okay.
>> Yeah. Yeah. Yes. I see it. I see it.
I thought in maths.
>> No. I just show you this all the time in class. So C is equal to 90 T. Now instead of using C and T, I will just use Y and X, right? So I will say Y is equal to 90X, right? Let me just Okay, cool. So I have that I have that graph over there, right? People on Tik Tok can't see it. So I'm showing some proof here using GeoGebra. And then we have y is equal to 80x + 50.
So when I press when I press the inter even on this it kind of had um see the point of intersection.
All right. Are you see any point of intersection there? Yes or no?
>> Yeah. Yeah. Yeah. I think so.
>> Okay. When I press the point of intersection, all you could tell me what I supposed to get. Anybody could tell me what I was supposed to get.
>> Is it supposed to get five and 450?
>> Bam bam bam bam bam. You see? Watch.
Badness, right? Badness.
>> Yes, sir.
>> Yeah.
>> Just can't use this in the exam.
>> Unfortunately. Unfortunately. But um let me do a quick recap. Right.
So in the question they gave you a table and this table was representative of Plaxton's rates and fees. So you're seeing length of our length of our job in hours and you're seeing the cost you saw that the cost is increasing as time increases. So it kind of looks like our hourly rate because the cost increases by the same amount 80. So just from that, we could kind of figure out that the that the hourly rate is $80. If you were to backtrack a bit and take away 80, you see 50 and that would kind of give you the inspection fee. Now, anytime the rate of change is the same, you should already be thinking about a line, a straight line, a linear graph.
So the first question was to plot was to plot a graph. So I plot the graph. Um the red line represents Plton's model.
So that wasn't hard. Part two, they wanted us to state the equation. On the y axis, we had co so replace y with c.
Um, instead of x, we had t. So, replace x with t. The hourly rate was 80. So, replace m with 80. And the y intercept was 50 because that's where the graph that's what the graph called the y axis.
So, I hope everybody understands that.
In part three, they ask us to say the inspection fee. The inspection fee is just the cost you had to pay one time is zero. So, that was 50 as the wind up.
Um, B, Black Plaxon received 490 for a job, determine the number of hours he spent on this job. So, what you can do, you could look at the graph or you could just plug in 490 into the model we came up with and solve for T and you get your answer over here. They mention a new person, Leela. Leela works a bit different from Plaxton, right? If if it gives you the job, you don't have to pay any inspection fee. If you don't give her the job, you have to pay an inspection fee of 50. But in this question, they said assuming that she's given all the jobs. So if she's given all the jobs, then she just has to pay $90 per hour.
So the model there is just C is equal to 90 byt. So every hour that goes by, we had to pay $90 more. So they wanted us to plot the graph on the same graph as above, the one we did previously. So I get three points. I plotted the three points. Leela's model is in blue, right?
So I draw the red line for Plaxon and the blue line for Leela. Um in part two they ask us how long would it take for both of them to earn the same amount of money. And anytime you see a question like that you're thinking about intersection. You look at the intersection you see is 5a 450. So when both of them work for 5 hours both of them are getting the same amount of money. Both of them are getting the same amount of money. Somebody is asking me what y is equal to mx plus c. y is equal to mx plus c represents a linear relationship here. What? Watch the video. Watch the watch the um video on YouTube and you're going to understand it. We're real into it now. So I don't want to go back to that. But it represents a linear relationship.
Um the YouTube live. You guys not hearing me on the YouTube live. Give a second.
Um, soundtrack one.
Okay, I'm not sure what's going on with the YouTube live edits. Um, customization.
Yeah, I'm not sure what going on there.
Yeah, I really not sure what going on there with the H and just showing your face like the [ __ ] >> Okay. Well, I had to work on that, right? Um, for now, we will just focus on the Zoom, right? Or we will work on that. I feel like it just makes sense to end the YouTube live because like it's just ping resources on it not working out. Um, people that want to join the meeting, um, head over to Tik Tok on the live.
Head over to the live and you should find the meeting information somewhere there, right? But sorry about that. I will work on the YouTube live.
Okay, let's continue.
So, part two, I need a volunteer for this. Let me just give a second share.
Okay, you guys seeing your screen, right? Cool. Um, somebody give us anything.
>> You see your screen now?
>> Yes, please.
>> Okay, I want somebody to give us a read from now. Give this question a read.
Ella wanted to determine the characteristics of a great teacher that are important to a group of 30 fm students at her school. She asked the students to rate the importance of each of the following five criteria using a scale of 1 to 10 with 10 representing a characteristic that is most important and one representing a characteristic that is least important. Entertaining, communicative, knowledgeable, caring, easygoing. The students ratings for entertaining are shown below. You're required to write a description of how the investigation would have been conducted by using the headings provided and answering the questions that follow.
Determine the range of the ratings for the data reported above.
>> Right? So, we have to determine the range. So I see Nikolai raise his hand.
Nikolai talk to her.
>> There's just something to say. You know how she read all of that? You know, like in the English test where you have to do the five main points and write a summary.
>> I'm looking.
>> Yeah, boy. I don't you see paper three in maths is like an English test as well because it's uh it's application type questions.
So you're going to have to do a lot of reading which is annoying in maths. So let's answer the question. Determine the range of the ratings from the data recorded above. So does anybody know what the range is? Range. Does anybody know what range is?
>> Is the highest observation >> minus lowest.
>> Huh? So what was the lowest score?
That that what was the lowest score from the data recorded above?
>> Seven. Seven.
>> Yeah. And what was the highest score?
What's the highest score?
>> Um, 10.
>> 10. So, that was going to be 10 - 7.
What's 10 - 7?
>> Three.
>> Cool. That was easy.
>> That was an easy one. Mark, right? I feel like we back in standard five.
Complete the tally and frequency columns in the table below. So, if any of you all forgot how tall is work, you're going to if you want to write five, you're going to draw four sticks and then you're going to cross it. Do you all remember that or no?
>> Yes.
Yes.
>> Okay. Cool. So, seven. Let's Let's count the amount of times we saw seven. Seven.
Seven. Seven. Seven. Seven. Seven.
Seven. How much times is that?
>> Seven times.
>> Seven times.
>> Wow.
That's that's funny. So, it happened seven times. So, to represent seven is going to be 1 2 3 4 cross that be five.
Then two more to indicate seven. Did you guys understand that?
>> Yes.
>> Yes.
>> So we recorded a rating of seven seven times. So that's going to be four with a cross to represent five and then two more.
Cool. Nine. Let's count nine now. So nine.
Three nine. Well, four nines, >> right? Four nines.
to represent four nines is going to be one, two, three, four. Is there anybody that's going to Is there anybody here that's going to lose at three marks?
>> No.
>> No, sir.
>> You sure? Right. If there's anybody here that wants me to go over the tally chat, let me know. But everybody Okay. Let me know if you're good.
>> Understood, sir.
>> Okay.
>> Like that person. I fully understand it, sir.
>> I fully understand it.
>> I fully understand.
Yeah. Uh so part three using the table above determine for the 30 students on the entertaining attribute of their teacher the median rating. Okay. This is something that has confused real people but essentially the median is like the middle is like the middle data point. So I'll explain what I mean by that. So the median is Q2 and Q2 is going to be represented by half N + 1 term. So stay with me. It'll make so much sense just now.
Okay. Let me give a quick example.
Right. Imagine I had one, two, three, four, five. Could anybody tell me what the middle data data point would be? The middle >> three.
>> That is what the median no that is all the median asking you. The median asking you for the middle value in ascending order. So your data has to be in ascending order and it just be given by the middle value. That that's literally it. Okay. And what if you had um what if you had like even set of numbers like 1 2 3 4? Could anybody tell me where the middle number would be?
>> It would be the average of those two numbers.
>> Yeah. Are they seeing that? The middle >> average of two or three.
>> Exactly. So I hope you guys understand why the formula says um Q2 is equal to half n + one. Because what we ended up having to do here is finding half of five. Where's half of five? Somebody tell me where's half a five? Half a five is what?
>> 2.5, >> right? 2.5. If it's 2.5, that would be in between the second term. Andy, >> third term.
>> Third term.
>> Isn't that where you observed over here?
The middle was in between two and three.
>> Yes sir.
>> Yeah. So the median is just going to be in the middle of your data of your data.
And your data needs to be in ascending order. So hope we understand that.
So we have 30 students. So n represents the total number of students you have.
So that's going to be a half of 30 + 1.
What is a half of 30 + 1? Somebody tell me where's a half of 30 + 1 >> 15.5 >> 15.5 Now here they tell you that 15.5 is not my answer. Is not my answer. No.
Naughty. Naughty. If you think that is the answer, no. That tells me where the answer is. It be the 15.5th term. So that'll be in between what terms?
Somebody tell me fast. That'll be in between what terms?
>> 15th and the 16th.
>> Everybody okay with that? Between the 15th and the 16th, too.
>> Yes, sir.
>> Okay. Good.
Now, let me show you guys a very easy way to work this question out. So, I'm going to create another another um a second. I'm going to create another column and I'm going to call that cumulative frequency. You'll see why I'm doing this. Cumulative frequency is just the running total of the frequency. If you're confused, don't worry. You will understand just now. So, we starting off with seven and then if you add the 18 other people, we'll get over here.
Okay. So, just to make sure we understand this, does everybody understand that frequency tells us the number of people? Yeah, I don't know.
>> 26.
>> 26.
Nah, we 20.
>> Are we 25?
>> 25. Right. My bad.
>> Right. 25. So, let me explain what we're going on here. Right. The first seven people would have would have give a rating on a what? The first seven people would have give a rating on a what?
>> Seven.
>> Seven.
>> The other 18 people. The next 18 people would I give a rating on what?
>> Okay. So the so if you combine seven and 18, right? Any 25 people over here, would I give a rating of either eight or seven?
>> Yes, sir.
>> Yes, sir.
>> Okay, good. And now if I wanted to figure out the amount of people that give a rating of 9, eight, and seven, how would I do that?
>> Yeah. Add the four to the 25.
>> Exactly.
And if I wanted to figure out the amount of people that give a rating at 10, 9, 8, and seven, what would that be? What would that be?
>> 30.
>> 30. So, I'm going to go over the cumulative frequency one more time. Just note it's just a running total.
I don't mean like you say in both. I mean like you're going to add the frequencies.
Cool. So, let me start over. So, Sarah, how many people give a rating a seven?
How many people give a rating a seven?
Seven.
>> Seven. Okay. How many people give a rating of eight?
>> 18.
>> 18. How many people give a rating of eight and or seven >> exactly? So I hope I understand that. If I wanted to figure out the amount of people that would have give a rating of seven and eight, I would need to add seven and 18. So that would give me 25 here. If I wanted to figure out the amount of people that give a rating of 7, 8, and 9, how would I do that?
>> 25 + 4.
>> Good.
>> Everybody in class understand cumulative frequency. Yes or no?
>> Yes.
>> Yes, sir.
>> You're probably wondering, sir, how going to help me here? Well, let me show you. Right.
The first person all the way to the seventh person, would I give a rate or what? Somebody tell me. Seven.
>> Okay.
>> Seven.
>> The eighth person all the way up to the 25th person would have given a rating on a what?
>> Chains.
>> I write seven boy. Oh, that's not a seven. It's just a arrow. Just an arrow pointing.
It looking like a seven. No. Yeah. 8 to 25. Give a rating on what?
>> 18.
>> 18. Nah. Nah.
Eight. Yeah. Eight.
The next person which is the 26th person all the way up to the 29th person would have given a rate on a what?
>> Nine.
>> Right.
>> My bad.
>> The last person would have given a rate on a what? The last person would have given a rate on what?
>> 10.
>> 10.
>> 10.
>> All right. I'm going to run through this process one more time. Right. I go in somewhere with this. If you're confused, don't worry. are going somewhere with this. So, okay, the first seven people, they gave a rating of seven. So, that would be the first to the seventh person. Cool.
The eighth person all the way up to the 25th person would have given a rating at eight. The 26th person all the way up to the 29th person would have given a rating a nine. And the 30th person all the way up to the 10th person would have given a rating a 30. I say not not 30, right? Um the 30th person would have given a rating a 10. If there's anything confusing you here, just tell me. I'll reexplain it.
I streaming every day after the seventh of May. After after the seventh of May, I'm going to be here doing free Zoom meetings, free lives every every day.
Every day. So, seventh of May. Yeah. Um, is there anybody that doesn't understand how I did this?
>> Yes, sir. I understand, sir.
>> S, you understand?
No sir.
>> Nah.
Nah. Oh yeah.
>> Yeah.
>> Yeah. Okay. Nikki. Nikki. Let me know if you understand if you're confused.
>> Yes, sir. I understand this.
>> Okay. Shantel, Romano, Akira, Camille.
Are you understand?
>> Yes, sir.
>> Yes, sir. Right.
>> Cassidy, Alen, Ambika.
>> Yes.
>> iPhone. iPhone. I see two iPhones in class.
Oh, are you even kidding? Right. Watch.
Two iPhones in class. Yeah, we have like a iPhone 16 or iPhone 13. What we are?
All right. Um, Sadika, Lucas, Abish, >> CC.
Are you understand this?
>> Yes, sir.
>> All right. Yes, sir.
C CC Keanu Rei Kay Daniela people here but are you understand right?
>> Yes sir.
>> So like our median was in between what?
What values? Somebody tell me. It was in between what? It was in between >> 15 2016.
>> It was in between 15 and 16. So where would 15 and 16? 15. Between 1 to 7 18 8 to 25 >> 8 to 25.
Right. So does do all of you guys understand that from the eighth person to the 25th person everybody would have given a rating of eight. Right? Are you understand that?
>> Yes sir.
>> Yes.
>> So >> tell what would the 15th person have given a rating of? The 15th person would have given a rating of what?
>> Eight.
>> The 16th person would have given a rating of what?
>> Eight.
So if both of them given the same rating rights any median would just be eight.
>> Yes sir. Yes sir.
>> I really hope all you understand that you know and here while we on this topic are you want me to explain Q Q3 Q1 one time or no?
>> Yes sir.
>> Yes sir.
>> Okay no problem.
>> Yes sir.
>> Yes sir. Please.
>> So does everybody here understand that?
Okay. Okay, the eighth person all the way to the 25th person. All of them given a rating are eight. So in this range it would also include the 15th and the 16th person. So what does this mean?
It means that the 15th person would have given a rating of eight and the 16th person would have given a rating of eight. So I hope you guys understand that. So if you find 8, so to find for Q2, Q2 would just be 8 + 8 all over 2, which we know going to be 8.
All right. Are you sure you understand that? Yes or no?
>> Yes. Yes.
>> Yes, sir.
>> Okay. I taking all your word for it. So I'm going ask a question, right? What did the 28th person give a rating of?
Let me see if I really understand this thing. The 28th person.
>> The 28th person.
>> Nine.
>> Nine.
>> Right. Because I would be in between the 26 and the 29th person. Nine. Okay.
Okay. I see getting good at this. What would the second person have given a rating of? The second person.
>> Seven.
>> Yeah. Because that would be in between one to seven. Cool. Cool.
I see somebody join the the Tik Tok with a funny name boy.
It be hard not to laugh and think you know. But anyways, >> what about the the ninth person? The ninth person would give a rating on a what?
>> Are they sure they understand this and hearing people like Matias, >> Reesei, Amelia, Josiah on this zoom like I escaping you know I here to help you in any way I could. So I call >> you so you can just repeat like the um the topic cuz I just joined to like refresh >> that would be kind of hard right. So I just I'll just explain it quickly.
>> Um you know how cumulative frequency does work. Yeah.
>> I think so I have a idea but I don't know how to explain it.
>> All right. So watch um seven people give a rating a seven. Right. So we start off with seven.
Eight people give a rating of 18. So 7 7 + 18 25. So what does the 25 mean? So Josiah, the 25 would tell you the amount of people that give a rating of 8 and seven. You understand?
>> Yes, sir.
>> Josiah, if I wanted to figure out how much people give a rating of of seven, eight, and nine. How would I do that? 7, 8, and nine. How I doing that?
>> Um, I'll add it up.
>> You can add 25 to what? Um 25 to nine.
>> Nah.
>> Tell me how much people give a rating on nine. What was the frequency? Frequency is the amount of people. How much people give a rating on nine? Four. So if 25 people will give a rating of seven and eight. Then to add it to nine, I would add four cuz four people give a rating on nine. So 29 29 people would have would have given a rating of 7, eight or nine.
Um, >> tell me something right Josiah the 30th person would have given a rating or what?
>> Um, >> 10.
>> Yep. Yep. Yeah. It seem like you understand it. What What do you think the the ninth persons would I give a rating of?
>> The ninth person um eight.
>> Big up yourself. Big up yourself. Yeah.
>> Yes. Yes sir. Cuz I didn't pay.
>> Okay. Okay. Well, um, you check back this recording when I finish. I'll go over everything in real real detail by real detail.
>> Okay, thanks.
>> Okay, let me look at Q1 now. So, to make this make sense, this is the nor normal distribution for data, right? I'm going draw it back. This is the normal distribution for data. Kind of looks like a hill.
This over here would represent Q1. This over here would represent Q2. And this would represent Q3. Now Q2 and so they can see that is the medium that cut any data in like at the middle point.
>> Yes sir.
>> So this a quarter this is two quarters which is a half. This is three quarters and this is four or four. So if all you had to say Q1 would be like what Q2 was a half right? What do you think Q1 is?
What do you think Q1 is?
>> Q1 is a quarter. What do you think Q3 is?
>> Three quarter.
>> Three quarter.
>> Yeah. Yeah, I really hope I understand that. So Q1 would be a quarter of N + one and this would tell you the position of the lower quartile Q1. Yeah, should I probably say that this represents the lower quartile.
This is the lower quartile, right? Q1 is equal to a quarter N + one. And so remind me what was the total number of students?
was 30, right? Was 30. So if I want to find the position of the lower quartile, that's going to be a quarter of 30 + 1.
Somebody tell me how fast that quarter of 30 + 1 big up yourself.
>> 7.75 7.75, right?
>> I guess 7.5. Okay.
Let me plug that into my calculator.
No, no, no.
7.75.
>> Okay, let me verify that's >> okay. So, I'm ask that question, right?
7.75.
Really? That would be in between what two values at the end of the day? What two whole values I would be in between?
>> Seven and eight.
>> Everybody Everybody that that makes sense, right? 7.75. That's going to be in between these two whole numbers. So it wouldn't be exactly in the middle, right? But it going to be in between seven and seven and eight. Not exactly in the middle, but I'll probably get a point.
This be seven will be over here. Eight would be over here. 7.75 somewhere in the middle.
So 7.75 in between seventh term and the eighth term.
Cool. Hope that makes sense.
So let's look at our table now. Could somebody tell me what the seventh person would have given the rating as seventh person?
>> Seven.
>> Yes. So the seventh person would have given a rating of seven. Could anybody tell me what the um what the eighth person would have given a rating of >> eight.
>> Eight. So if I wanted to find for Q1 >> what it would be 7 + 8 / 2.
>> Correct. 7 + 8id 2. 7 + 8id 2 is what?
>> 7.5.
>> Okay, cool. Now, I want somebody that's confused to do Q3 with me. There's anybody that's confused, we could potentially look at Q3 together.
Okay, I'm not hearing anybody confused.
That's good and bad at the same time.
Somebody definitely confused and I just don't tell them. So, we want to find Q3.
So somebody tell me in the data over here Q3 is going to tell you the what value like the half mark the 3/4 mark what >> yeah that would mark so that's going to be 3/4 of >> one right and um we know that the the total amount of students here is 30 so that's going to be 31 where is 3/4 of 31 3/4 of 31 was that 3/4 of 31 23.25.
>> Are you getting >> 23.25?
>> 23.25.
Now the 23.25 term. Really? That'll be in between what? Two whole numbers.
>> 23 >> 23 and 24.
>> 23 and 24.
>> Oh, you understand that right?
>> Yes sir.
>> Yes sir. So somebody look at the um look at the table and tell me >> what's rating would the 23rd person have given the 23rd person?
>> Eight.
>> If you're confused, look at the range.
The eighth person all the way up to the 25th person give eight. So if we're talking about the 23rd person, that would be in between that range 8 to 25.
So they would have given a rating of eight. Um what did the 24th person give a rating of?
>> 24th person.
>> Eight as well. eight.
>> So to find for Q3, you know that the 23rd, the 23rd term is 8. The 23rd term is 8 and the 24th term is also 8. And so if you find Q3, Q3 would just be the average of that. 8 + 8 over 2. What is 8 plus 8 over two, guys?
Eight.
>> Eight.
>> Eight. Cool. And so do you guys feel like you know how to find for Q1, Q2, and Q3 now?
>> Yes sir.
>> Okay. I want to go over this procedure one more time because it makes it so simple and just students don't fully understand it. The first thing I I'd recommend is finding the cumulative frequency. Let's just say running total.
So 7 starting off with seven. You don't need to add to that. So I write back seven. Then I say 7 + 18 25. Then I say 25 + 4 29. 29 + 1 30. The last value for your cumulative frequency should be the total amount of people because you're adding up everybody. If all you notice the what was the number of children?
What's the number of children?
>> 30 was 30.
>> 30.
>> If you do cumulative frequency correctly, the last value is going to be the total number because you would have added up everybody.
Okay. The next thing you see the seven over here that tells me the first person all the way to the seventh person give a rating a seven. The next person which is the eighth person all the way to the 25th person would give a rating at eight. And I just just continuing the the pattern over there. And with this we can figure out Q1, Q2, Q3. Real real easy. Real easy.
So again here's our example. Q3 23rd that's between 8 and 25. You give a rating on an eight.
24 that's between 8 and 25. Give a rating on eight. So I feel like you understand Q1, Q2 and Q3.
Yeah.
>> Yes sir.
>> Yeah. Okay. Okay. I taking all your word for it. I taking all your word for it.
>> Yes sir.
>> Okay. I'll let you know if it have anything confusing here. I'm lowkey very patient and so I'll I'll go it over as much time as you need me to to fully understand the thing.
Okay, so I see somebody on the Tik Tok say do it back. Um, people on the Tik Tok, I recommend it to go and watch the video on YouTube. Like people on the Zoom though, if you're on the Zoom, you could ask me cuz I can write here and I can show you it. Have like a bit of miscommunication with Tik Tok.
Better to do it on the Zoom.
So um let's just run through the rules quickly. If I wanted to find for Q1, Q1 will be what? How do I find the position on Q1? Tell me fast. Quick, quick, rapid speed. Q1 >> a fourth and n + one.
>> Yeah. Quarter n plus one. That would tell me the position on Q1. How would I find the position at Q2?
>> Uh N + one.
>> Half N plus one. Bam. Position on Q3.
How doing that?
brackets.
>> Now, if you get a a a number with a decimal, like let me just say you get 2.75, right? The 2.75th term, then that number would have to be in between what terms?
>> 23.
>> So, you'd find the average of the the second and the third term and you get your answer.
So, I really hope you understand that.
And again the reason for this is because you can imagine if you have a data set over here and you put down three you put down three markers this would represent the quarter mark in your data that's Q1 that's why Q1 is a quarter this would represent the half mark in the data cuz this will be 2 over 4 right 2 over 4 simplifies simplifies to a half and well this would be Q3 this would represent 3/4 of your data so 3/4 n + one so hole and um with this information you could find for interquartile range. Does anybody remember what interquartile range is? Interquartile range.
>> Q3 minus Q1.
>> Yeah, that's what IQR is. IQR is Q3 minus Q1. How much of you guys knew that?
Did you guys know that?
>> Yes, I knew. No, I didn't.
>> Well, now you know, right? Now you know.
So, the person that said it didn't know that. What do we get Q3 to be?
We got Q3 to be what?
>> Q3 that would be 22.
>> No. Um, >> that is eight. So, let me explain it to you quickly. Right. This formula over here, it doesn't tell you the answer straight away. It tells you the position of your answer. So, when we found 3/4 of 31, we got 23.25. 23.25. That's in between what two numbers?
>> The 23rd and the 24th number.
>> Exactly. So now you're going to look at your table and you see that the 23rd and the 24th number both of them in that range. So the 23rd person and the 24th person would rate our eight.
>> Eight.
>> Yeah. And so 23rd is 8. 24th is eight.
Just find the average of that. 8 + 8 / 2 8.
So that was Q3. And well for Q1 we found that Q1 was 7.5 because the seventh term give a rating of seven. The eighth person give a rating of eight. So 7 + 8 divid by 2 7.5.
Oh look Mrs. Math Vibes join exposure. I'm going to expose you. I wouldn't expect >> Yeah. So Q3 So Q3 is eight. And where is Q1?
Somebody tell my Q1. Where's Q1? What is Q1? What is Q1?
>> 7.5.
>> 7.5.
>> So where's 8 minus 7.5 >> 1.5?
>> No, that'll be 0.5.
N 1.5.
>> So I hope everybody understands how to find the median now the lower quartile and the upper quartile.
And I hope you understand how to find interquartile range.
Yes sir.
>> Cool.
Um part B now or somebody's mic is unmuted and we're hearing you >> said that was me. Sorry.
>> So okay the other part of the question is they want us Wait. They didn't copy.
Come on.
Delete this.
Okay. Let me just copy this real quick.
Copy.
Paste. The other question. They want us to find the average.
They want us to find the average. And that is so much easier than any of you all could think of. So when we look at average, right? I'm going give example.
We just say we had 27 9 and 10. How would I find the average for that for that set for that set of numbers? How would I find the average for that?
>> Yeah. So you say 2 + 7 + 9 + 10 and you divide that by what? What you going to divide that by?
>> Cool. And you get your answer, right? So generally speaking, the average or the mean or Xbar is just the total the total all over the number or the frequency the the um sum of the frequency which is like the total amount of participants. So total number of participants or like just total number. So like you see I add up 2 7 9 and 10 right? So I add up all the elements in the in the set of data and I divided it by the by the number by the number of data I had.
So I had like 27 and 10. So I add four data add four values for data and the sum of that is 27 and 10. Yeah. You plug into your calculator, you divide by four and you get your answer.
Um somebody asked me what's the difference between average and mean.
Average and mean mean the same thing, right? I'll make a note about it over here. They mean the exact same thing.
So average, mean, xbar, all mean the same thing. All mean the same thing. No difference. Just the same way writing the same thing. Just it's like it's like okay. It's like calling somebody pretty. They can call them beautiful or bonita. I mean the same thing. I say that because mrs math Mrs. Math vibes is um in the meeting.
That's why that's why using words like that. Yeah.
Yeah, surely vexed now cuz I talked to [ __ ] Okay, everybody all right with everything's over.
>> Yes.
>> So you know how to find average now, right?
>> Okay. So if I give all one If I give all one, two, three, four.
>> Yeah, you could use sigma fx over sigma f. I'm going to I want to introduce the students to the concept. I want to explain the concept behind that. So if you had 1 2 3 4, how do you find the average for that?
>> Add them up and divided by four.
>> Exactly. Exactly. So you're probably wondering where I'm going with this. I really want to teach you guys the concept here. So remember to find the average is the total amount divided by the amount of people. So when you look at this, how many people got a rate on a seven?
>> Seven people. seven.
>> So if you wanted to find the total amount for that for that rating, you'd multiply seven by seven, right? And you get seven by what? 7 by 7? Where 7 by 7?
>> Okay. Here what I'm I'm going to reveal the formula at the end when you guys understand the concept because once you understand the concept, you don't have to remember any formulas because the formula comes from a concept. If I wanted to find the total amount of returns, granted that 18 people give a return on eight. How doing that? How can I find the total amount of returns?
>> You can repeat please.
>> Okay. How many people give a rating of eight?
>> 18.
>> So if I wanted to find the total, how am I doing that?
>> 189 + 18.
>> Now I got to multiply 8 by 18 because think about it. 18 people. 18 people, right? One person, another person, another person, another person, another person, another person. 18 people. All of them give a rating of eight.
So altogether, if you want to find the combined rating, you multiply 8 by 18.
What is 8 by 18?
>> 144.
>> 144.
>> Well, you understand where I'm going with this? Because like watch if the data wasn't wasn't grouped together in wasn't wasn't in this format, right? If it was raw data, you would see that you'd have seven sevens.
Then you would have 18.
And so you'd have to add all of this and divide it by the total amount of students is the same thing we're doing here. So 18 people would have vote eight. So 18 by 8 144. If four people vote nine, how do I find the total amount of ratings for that?
>> 9 by4.
>> Exactly. Where where's 9 by4?
36.
>> 36.
>> All right. And well, how many people are rating out of 10?
>> 10.
>> So, does everybody understand? Now, what I'm doing here, I'm really trying to find the total.
>> Yes, sir.
>> If you're confused, seven people give a rating a seven. So, altogether that's 7 by 7 at 49.
18 people give a rating at 8. 18 by 8.
144. So the total amount is 144 and I just do that for the rest. Does everybody understand that? Yes or no?
>> Yes sir.
>> Okay sir.
>> So if if I wanted to find the total number the total number how would I do that? Somebody tell me.
>> Sorry.
>> Add up all.
>> I just had to add up all. So and when I add up all wouldn't that tell me the total number of ratings like the sum of all the ratings?
>> Yes sir. Yes sir.
>> That's where you would tell me. And then I would just have to divide that by the number of what >> ratings.
>> Yeah. How much ratings I had?
>> 30.
>> 30.
>> And that's it. Isn't that the same concept as surely where you 1 2 3 4?
Real simple example.
>> Yes sir.
>> It's the same concept.
>> All right. So when you add up all that again what you get for 49 plus >> 20 what?
>> 39.
>> Uhhuh. So if you wanted to find the average right? So 239 is all the ratings add up together. Now how much students vote?
>> 30 >> exactly. So if you wanted to find the average um that would just be equal to 239 divided by what?
30.
>> Okay. And what we get? What's 239 over 30?
>> 7.97.
>> Yeah. Seven.
>> Right. Give me your answer to three significant figures.
>> 7.97.
>> Yeah. 7.97.
Now a lot of you guys would have learned this formula in school but you really didn't understand why it is do it you know. So the frequency is f for those that didn't know the frequency is given by f. Now the rate in here this is this is like what we're measuring whatever you are measuring you call that x that's the variable that's where you're measuring. So in school you would you would learn that you had to find fx and then you'd have to find the sum of fx.
And lastly, you have to find the sum of f, which is the sum of all the frequencies. And in the end, your formula should look like this. And this what you learn in school. The sum of f_sub_x all over the sum of f.
Now, the reason why I kept the formula away is because I wanted you guys to actually think and see how they come up with a formula. I feel like all understand how they come up with the formula now like a little bit.
>> Yes, sir.
>> Yes, sir.
>> Yes, sir. So let me run it back again.
Yeah. Here what? So you said the formula total divided by the amount of numbers is for when here what right for mean two. All of it is the same thing. All that is the same thing. Right. Is the exact same thing. The reason why you have to find sum of fx over here is because the data is kind of arranged like grouped is like condensed. It's not raw data. If you look at it seven people got a rate and a seven. So all together if you wanted to find the total number for that you multiply 7 by 749. So like with this you first have to multiply to find the total and then you have to add up everything to find the total total.
I'm not sure that makes sense. Um and I think all you understand why I had to multiply the frequency by the rating.
Let me know if you understand that.
>> Yes sir.
>> Are you confused please? Somebody said they confused. Okay, talk to her. I'll I'll go over the whole thing and you will understand. Trust. But talk to her.
Yeah, somebody said they was confused.
Okay, let me try to go over the concept quickly. Nikolai, there >> sir.
>> Nikolai, when you're finding average, right? Average for raw data and you would just add up all the data.
Yeah. add up everything and you just divide it by the number.
>> Yes sir.
>> Okay, cool. What if I told you it's the exact same concept here? So tell me Nikolai, how much people got a got a how much people gave a rate on our seven?
>> Seven.
>> So altogether was the combined rate on them when you add up everything?
>> It'll be 49.
>> Exactly. If 18 people gave a rate on eight, how much did they give all together?
144.
>> Exactly. Aren't we just finding the totals?
>> Yes, sir.
>> How much people gave a rating a nine?
>> Four people.
>> So, what be the total then?
>> 36.
>> Okay. How much people give a rating on a 10?
>> One.
>> Right. So, if I wanted to find the total number for the ratings, what I had to do, >> you would have to add up all the the terms that we found out for.
>> Exactly. And then you would just divide that by the number of students which is really just the sum of the frequency because the frequency is the number of students. So when you add 7 18 4 and 1 tell me what are they getting? What is 7 + 18 + 4 + 1? What is that? What is 7 >> exactly 30?
>> So that's why in school they would have learned this formula sum of fx over sum of f. The real reason you're using this formula here is because you first need to expand out back the data. You need to see what the total for each row would have been. So seven people gave seven.
So 49 18 people give you a rating of eight. So 144.
So that's why you have to multiply the frequency by the by where you're measuring the variable.
And that's why you have to add it up because you want to find the total. And then you would divide that by the number of students or the amount of participants or just the total frequency. Does everybody understand?
Yes or no?
>> Yes sir.
>> Yes sir.
>> Right. Could somebody in class just tell me what sum of f is quickly?
>> What s of f? Where's sum of f? Sigma f.
>> Does everybody understand why sum of f is 30 or no?
Yes sir.
>> Okay. If this symbol is confusing you, all it means is I going to add. That is all it means. So like you see how I get 239. That's because I summed what it means. I mean summed. I summed all the elements I got for FX.
So that's how I got the 239. And that's what this sigma that's what this symbol over here represents. It's called sigma.
And it just tells it's just telling you that you had to sum each element. So 49 + 144 + 36 + 10 you get 29 political you understand this or not >> if you don't understand just tell me >> yes >> okay I take all your word for it all you understand right so the work I present in the exam you would have said the sum of fx all over the sum of f and remember the sum of fx is the total number right and to find the total number you had to multiply the frequency by the variable so 7 by 7 49 18 by 8 144 etc you add up all that and you'll find the total number of all the ratings combined and then sum of f is just the total number of participants so that'll be 30 and yeah you get the 2.97 so is there anybody what's in 2.97 that would be 7.97.
Yeah. Is there anybody that's majorly confused by this or you okay with it?
I see Nolan. Nikolai, you understand?
>> Yes, I understand. But there was a question I wanted to ask if they would provide a formula sheet although it's just two questions with a lot of parts in it.
>> Yeah. Yeah. They would they would present a formula sheet.
>> Yeah. Okay. But you are given a formula sheet for paper three. The exact same one you got for paper two.
>> Okay. So you don't really So all this is easy stuff once you know the formula and everything.
>> Nikolai, you don't even have to know the formula cuz you understand the concept of it now.
>> Yes sir. Yeah. 7 by 7 49 18 by 8. Add up all of that divided by the total. You understand the concept now? That's the most important bit.
Yeah.
So that's it for these types of questions. Um okay, cool.
Um any volunteers? Part C. Any volunteers?
I don't mind.
>> All right, give it a read.
>> I saw Camille mic. So I don't know if she wants to go.
Camille, I don't know if you want to do the question.
No, sir. I'll do another one.
>> You're skipping this one.
>> You're skipping this one.
>> Yes. I'm feeling so tired.
>> But if you wait to do another question, you get more tired.
>> All right.
>> Wait, wait. Let me hit you with the vibes. Let me vibes with the vibes. situated vibes right.
So in the question I read >> disable show some statistics for the five characteristics >> under consideration.
>> Mhm.
>> All right.
>> Hold on.
Five characteristics consideration.
>> Most of the statistics for entertaining are missing.
Statistics minimum rating, maximum rating, mean or average, standard deviation.
entertaining standard deviation 0.72.
>> You don't you don't have to read everything. You want to read everything.
>> Okay.
>> Leave out the column.
>> Yeah. Yeah. That's fine. That's fine. Um >> it's a lucky thing they didn't leave out standard deviation because to find standard deviation is real work. Anybody remember the formula for standard of deviation per purchase?
>> Isn't it the No.
is the square root of sigma f >> it's x - x bar squ >> all over n that's what it is that's standard deviation >> and well >> I miss the the x - x with the f >> now I don't have no f remember standard deviation tells you how your data varies with reference to the average so you would have to find x - x uh for all the data entries. So you see like how how far it is from the mean.
>> Yes sir.
>> Yeah.
But let me answer this question here because it's real simple and I don't think they going to make you do standard deviation. That's kind of evil if they do. But um here here what everybody here uh after the 7th of May I'll be doing free sessions every single day for like six hours and thing going to be crazy but going to be here to help however I could right you don't know math vibes to the world and I'll be very very in-depth and I'll take my time and I'll make sure you guys understand you know we we had to pass maths we had we had no we not passing maths we excelling in maths.
So Camille um they want us to state the minimum rating for entertaining. This real simple. What was the minimum rating for entertaining?
These were all the values for entertaining. What was the minimum value?
What's the what's the minimum value there?
Real simple. Promise.
Um >> seven.
>> Seven. That's it.
Yeah. What was the maximum rating?
What's the maximum rating?
>> Nine.
>> Nah, not nine. Was it nine?
>> I'm sorry. Um, 10.
>> 10.
And well, mean average, we find out already. How was the average?
>> Uh, 7.97.
Yeah. 7.97 was a hard Camille was hard.
>> No.
>> No. Camille. No. You see >> it's just it's the words is you know it's not >> it looking like a whole English paragraph. I mean not English I see.
>> I understand. Right. Analysis and interpretation of data.
Come on.
>> In order of importance to the students, the five characteristics are ranked from one to five with one being the most important and five being the least important. Given that easygoing is ranked number two and knowledgeable is ranked number four. Rank the remaining four qualities or >> remaining three qualities.
Sorry. The remaining three qualities.
>> All right.
So, um they already mark easy going and they already put knowledgeable.
Okay, cool.
So, we kind of need to Okay, here going to happen, right? I would advise you to look at the average rating because in the question, so let's look back at the question, right?
Ella wanted to determine the characteristics of a great teacher that are important to a group of 30 fifth form students at a school. She asked the students to rate the importance of each of the following five criteria using a scale of 1 to 10. So Camille, do you understand that our 1 to 10 tells the student tells you how important the students find that part of aspect is?
Yeah.
>> So I go I'll go over that one more time.
What does the rating tell us? The rating tells us how important the student thinks that aspect is. So if it's one, it's really low. If it's 10, it's really high.
Are you understand that? So does everybody does everybody understand that the rating tells us how important the students think it is?
>> Yeah or no?
>> Yes sir.
>> Yes sir.
>> Okay. So let me ask you a question, right? On average, which one had the most important rating? Like the highest rating?
Look at that. Which one had the highest rating?
>> Entertaining.
>> Yeah. Yeah. Entertaining.
Camille, let me know if you're saying that.
>> Yeah.
So Camille again if we want to see at a quick glance where is the most important thing and the most important one would have like the highest average rating.
>> Yeah.
>> So entertaining has the highest rating or if I was a teacher in school you think that I'll be entertaining?
>> Yes. Yes.
>> I probably do some real mad thing.
Probably do that.
Okay. What is the And I'll put something to the side. Right. Entertaining had a rating of 7.97.
Uh easy going on what?
>> Easy going.
>> I'm stubborn.
>> Okay. Um what you think I should put after easy going?
>> Karen.
>> Eligible.
>> N Karen. So we looking at the average rating.
>> Yeah. parent.
>> Imagine them them students scared the most about entertaining. Boy, way boy.
>> Know what my mind I was like um caring and easy going is they tie. So I didn't say that. I was just like you know probably the other one.
>> No no how to be caring. I had to be caring.
>> Okay.
>> How to be caring.
Yeah. All right. Um and hearing had a rating of 6.97 as well. And um knowledgeable had a rating of what?
>> 3.63.
>> And was the last one to rate? Was the last one?
>> Yeah. And that one had the lowest average rating.
Yeah. And communicative had a had an average or what? average rate on a what?
>> 3.3 >> 3.30.
Right, like I promised, I'm going to go over the whole paper quickly. Um, let me just make sure that I answered all the questions.
Um, here what standard deviation just tells you how spread apart the data is.
That's all it really tells you. That's what standard deviation tells you. It tells you how how spread apart data is with respect to the mean. So let me give you an example, right?
Data with a very low standard deviation would look like that.
Data with a very high standard deviation might look like that.
So, I'm not sure you see what I'm talking about, but if you're looking at the if you're looking at how the data is spread out about the mean, it's a lot more over here. So, this would have a high standard deviation. I don't see how that would really help us in this question because let me explain something right in the question, they literally told us that they're asking the students to rate from 1 to 10 the level of importance.
That's what they're asking. Again watch using a scale of 1 to 10 the importance.
So if we want to figure out what is the most important one we have to look at the average importance.
So hope you understand that. So on average um on average entertaining had the highest importance right on a scale of 1 to 10 entertainment was like the highest one. And then um after that we had easygoing then caring then um yeah then knowledgeable then communicative.
So if you like assets.
>> Yes sir.
>> Yes sir.
>> Yes sir.
>> Bet. Bet. Bet.
So let me run through the deep quickly.
Right. So in the first Oh Isaiah your mic on. All right. I see I see you mute yourself. Good.
All right.
All right.
So I see somebody said you can look at the standard deviation when the means are the same. That is correct because it would tell you how far apart and sparse the data is.
If so let me explain something right? If the means are the same you could look at the standard deviation. If the standard deviation is very low it would have meant that most of the students gave um gave a rating close to the average. But if it had a high standard deviation then there a lot of the students gave ratings kind of like they'd have give okay it would have been spread out it would have been spread out so that's why you could use standard deviation to make some inferences right okay and like the person said the lower the standard deviation the better and again the reason for that is because most of the data is really close to the mean if you have data that is kind of far from the mean, then it would have meant that some people give a high rating, some people give a low rating.
But if if the data is really close to the mean, then it would have meant that most of the students give a rating right around the same ballpark. So probably understand that.
So let me try to explain that back one more time so you guys could understand could understand that.
So first of all, do you guys understand what standard deviation is? You don't know.
>> Yes, sir.
>> All right. Let me see if I get I would have done this on my class the other day.
All right.
So, let me show you guys what a high standard deviation would look like and a low standard deviation would look like.
So, over here you see that this is a large standard deviation. And so, if this is the mean, you're realizing your data is very spread apart. Are you all seeing that or no? Let me know if you guys seen that.
>> Yes.
>> Now, if most of your data is very is very spread out from the mean, it would have mean that some people vote give like a low rating, some people give a high rating because it mean that the data spread apart.
But if you look at this right, does the data look like it's spread out far from the mean or looks very compact? It looks like it's very close to the mean.
If you guys had to see. So this is the mean over here. If you look at the data over there, does it look like the data is very close to the mean or far from the mean? If you guys had to say >> close, >> it's close. And if most of the data is close to the mean, it would have meant that most people give a relatively high rating or relatively low rating. And I should probably get what I saying.
So like let me give you a quick example, right? Say for instance people give a rating a um a one just say somebody give a rating a 9 10 8 7 10 8 when you look at all of those values over there those ratings ain't all of those ratings kind of high.
>> Yes.
>> And so when you find the average for that ain't you going to get a high average?
>> Yes.
>> Yeah you are going to get a high average. And because most of the data points were very close together, um if I tell you it have a low standard deviation, you can kind of figure out that most people give a high rating.
But let me show you something. Let me just say we had 10. We had 10 and we had one. Some people are beef with the beef beef with um this aspect. So they don't care if they're entertaining or something. 10 10 1 3 1 10. Uhhuh.
Look at this. I want you to compare that data to this data. Now over here the data is really really close together.
It's really really close together. So so the standard deviation will be very small because if you find the average the values are going to be very very like it's going to deviate slightly compared to the compared to the mean because most of the data is like around the same. But over here if you look at this let ask question right. If you look at this do you think that would have a high standard deviation or a large standard deviation? What do you think?
>> I >> you have a large standard deviation. You know why? Because look at the data.
Somebody vote at 10. Somebody vote at 10. Then somebody vote at one at three at three. A one and then a 10. So if you find the average for this um somebody find the average for that fast. Find the average and tell them what you're getting.
10 10 + 1 + 3 + 3 + 1 + 10 / by 7.
You should be getting 5.4 5.4 um three.
>> Yes, sir. That's what I get as I say.
>> Yeah. So, the average is going to be 5.43. But don't you have data that that like that varies a lot like okay some people vote one you know some people vote 10 so can you see how how spread out the data is >> the average 5.43 you know some people vote one some people vote 10 so if the standard deviation is large or high it tells you that the data is very spread out with respect to the mean understand that so what 5.43 4 three.
The lowest will be one, highest will be 10. Over here, I want you to find the average for this. I find the average for those data. So 9 10 8 7 10 and 8. Find the average.
9 + 10 + 8 + 7 + 10 + 8 and divide by six.
Let me know if I get something like >> 8.67.
>> Okay. Now when when I ask you what is the lowest value there you going to tell me what was the lowest value somebody say was the lowest value >> seven >> what was the highest value >> 10 >> so so were the was the data was the data spread out that much compared to the mean or was it close to the mean closer >> closer >> right so this would have a very low or small standard deviation because most of the data is like really close together.
But over here though, you're seeing that the mean is 5.43 and you can see that some people vote one and some people vote 10 on either end of the extreme. So you can see that the data here is spread apart. So this would have a very large standard deviation. So that is what standard deviation tells you. This would have a this would have a small standard deviation and this would have a very large standard deviation or if you like understand the concept of standard deviation.
>> Yes sir.
So that's why the person on Tik Tok would have said that, you know, if the mean is the same, you could look at standard deviation because the standard deviation would tell you how close the the ratings were together. So that's a brilliant point brought up by that person, right?
Cool. So you know what? Let me look at the standard deviation faster and see if we notice anything.
So, um, uh, Camille, both of these here had the same mean, right? Yeah, they're the same mean.
>> Yeah.
>> Okay. What was the standard deviation for easy going?
>> Um, 1.01.
>> What was the standard deviation for Karen?
>> 1.23.
Which which standard deviation is higher? Easygoing or caring.
>> Karen.
>> Exactly. So it would have meant >> Yeah. So it would have meant that the ratings for caring were a bit spread out but the ratings for easygoing were really close together. So it have been a bunch of a high values. I wonder if you understand now.
>> Yeah.
>> So Camille, one more time. One more time. So the higher the standard, the higher the standard deviation, the more spread apart your data is. The lower the standard deviation, the closer the values are together. So if you have the same mean, if you have the same mean, right, you have the same mean, but you have different standard deviations, you're looking to see which one has the lower standard deviation because the lower standard deviation would tell you that the data is like really close together.
Cuz Camille, which which instance do you think is better? People say 9 10 8 7 10 8 or 10 1011 one or 10 like that. Which which one? If people was given a rating, which rating would you rather this rating or this rating?
Somebody rating your business or something? Which rating? Which rating you prefer? Rating one or rating two?
>> Rating one.
>> Exactly. Are you understand what I mean?
If you running a business, >> would you want people to leave reviews like 9 10 8 7 10 8 or would you want them to leave reviews like 10 10 1 33 110 10? What would you prefer?
>> Second one.
>> Sure. I would prefer option one.
>> I would prefer option one. This is hear this.
This is raw. Let me explain something.
So if you're running a business, do you want to have a 10 a 10 star rating? a 10 star rating and oh a one star rating then wait my laptop going to die massac okay I save it last minute nice yeah so the person that said option
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