MEAN/MEDIAN/MODE PART-2 | Degree semester-2 Business Statistics UNIT-2 explanation part-2

[00:00:00]Hello everyone, welcome back to our channel Learn with Sahira. In this video, we are going to see the calculation of mean, median, and mode in continuous series. Continuous series is also known as grouped data. In our previous video, in our part one, we have seen the calculation of mean, median, and mode in discrete series. It is also known as ungrouped data. If you didn't watch that video, please go to my channel and watch that video. I will be sharing that video link in this video description also. If you watch both the parts, part one, my previous video, and part two, this video, you will be perfect with the concept of mean, median, and mode in both the series, discrete series as well as continuous series. Whatever the question they may give you in the examination, you will be able to do the solution and easily you can score full marks. So, if you just watch one video, that will be not okay.

[00:00:53]Because sometimes in the examination, they will be asking continuous series.

[00:00:56]Sometimes they will be asking discrete series. So, if you will be perfect with both the series, then only it will be okay. Formulas will be different, but the procedure will be same. Okay, so let us get started. But before starting, I must say you that if you're new to our channel Learn with Sahira, subscribe it for more videos and don't forget to share this video with your friends, too.

[00:01:17]And if you want the notes of all the subjects and languages, whatever you are having in your group, I will be giving you the access for all subject and languages important question and answer notes, which are easy, simple, and clear to understand. If you want the notes, let me know on my Instagram, drop me a message want notes. I will be giving you all subject notes, okay? Uh my Instagram ID is Learn with Sahira. I will be mentioning my Instagram ID link in this video description also. Note, payment is must. I repeat, payment is must. Okay, so without getting late, let us get started. First, we will be calculating mean, then we will be going to median.

[00:01:55]In the last, we will be seeing mode, okay? So, whenever you are calculating something, whatever it is there in the question you have to take it, okay? We are having marks column as well as number of students column. So, we took marks and number of students the same way you have to take in your solution also. See here, they have not mentioned X and F. Sometimes they will be mentioning, sometimes they will not be mentioning. If they didn't mention, you have to take marks as X.

[00:02:22]Number of students as F. Okay. And whatever they have given in the question, you take that, okay? Marks, first one is uh sorry, it is 0 to 10.

[00:02:32]Okay. 0 to 10, this is nothing. 0 to 10 10 to 20 20 to 30 30 to 40 40 to 50 Okay. Then number of students you have to take as it is, three eight 12 seven two. Okay. Now, you have to calculate or you have to see the mid value.

[00:03:01]Okay? When you are calculating mean in continuous series, you have to go with mid value. But when you are calculating mean in discrete series, no need to go with the mid value. In our last video already we have discussed about discrete series. Now, let us see about the continuous series, okay? Mid value is nothing but whatever the the number is lying in between both of these numbers, you have to take it, okay? Mid value from 0 to 10 is five.

[00:03:28]Okay. So, here uh 10 to 20, 20 to 30, interval is only 10, but sometimes if they give you 12, 18, 26, like that, what you have to do? You have to plus both of these numbers, like 10 + 20, it is 10 + 20, it is 30. After getting this number, what you have to do? You have to divide it by two. You will be getting the mid value. Okay, if they give like this, it will be really very easy to find out mid value. But if they give jumbled, then it will be hard or difficult. So, what you have to do, you have to add both of these values and divide it by two. You will be getting the mid value. For 10 to 20, mid value is 15.

[00:04:11]20 to 30, 25. 30 to 40, 35. And 40 to 50, it is 45.

[00:04:19]So, we got the mid value. Okay? Now, what we have to do, we have to calculate or we have to see FM.

[00:04:28]This mid value, let us assume it as M.

[00:04:31]Okay? FM, how we will be getting FM?

[00:04:34]When we multiply F with M, we will be getting FM. The value of F and the value of M, you have to take both the values and you have to multiply, not add. Okay?

[00:04:46]So, you can take a calculator. Don't do any mistakes. Better to do the calculation on calculator itself. 3 into 5, how much it is? It is 15.

[00:04:58]Then, 8 into 15, how much it is? 120.

[00:05:05]12 into 25, 300.

[00:05:10]7 into 35, 245.

[00:05:19]2 into 45, it is 90. Okay? So, we got FM also. When you calculate or when you multiply three with five or the value of F with M, you will be getting FM. Okay? In the answer booklet also, you have to draw a box like this. Okay? I'm just using the pen.

[00:05:38]In the answer booklet, you have to use scale and pencil. Clear and neat box you have to draw. Okay?

[00:05:44]Okay, so what you have to do now? You have to find sigma FM. Sigma FM is nothing but when you add all these values, you will be getting sigma FM.

[00:05:55]You add 15 + 120 + 300 + 245 + 90. How much it is? It is 770. Let us cross-check again. 15 + 120 + 300 + 245 + 90. It is 770. We got. Now, let us calculate N. N is also known as sigma F.

[00:06:17]You can take sigma F or you can take N.

[00:06:20]When you calculate or when you add all these numbers, you will be getting N. 3 + 8 + 12 + 7 + 2. How much it is? It is 32.

[00:06:31]Now, let us find the mean. Let us highlight these values with some other pen. I took red pen here.

[00:06:40]Okay, now what we are going to see? We are going to see the mean.

[00:06:44]Let us calculate mean. To calculate mean, we should know the formula of mean. What is the formula of mean?

[00:06:52]Formula of mean here is X bar equals to sigma FM by N.

[00:07:00]So, substitute the values into this formula.

[00:07:04]X bar equals to sigma FM, how much it is? It is 770.

[00:07:11]770 by 32.

[00:07:16]Okay.

[00:07:17]Calculate this 770 divided by 32. It is mean.

[00:07:27]Mean is how much we got, you see?

[00:07:30]24.0 You can take it as 24 also, no issues.

[00:07:37]Or you can also take it as 24.0.

[00:07:43]So, therefore, mean is 24. Okay, so this is our mean. Let us go with the median.

[00:07:52]median Okay.

[00:07:55]median Here median, of what we need to do first? To find the median, first we need to find the term. Okay. So what you have to write median the position the position of median class is n by 2.

[00:08:26]Okay. In a discrete series, we saw n plus 1 by 2, but here it is only n by 2.

[00:08:32]So what we need to do? We need to uh substitute the values. What is n? N is 32.

[00:08:39]32 by 2. Okay, so when we do the calculation, 32 by 2, what term or what number we are getting, we have to see.

[00:08:48]32 divided by 2. How much it is? It is 16. We are getting 16 here. So 16 is nothing but it is the term. Okay, 16th term. Okay, this is 16th term. To find 16th term, we need to find cumulative frequency.

[00:09:08]Whenever we are finding median, we should find cumulative frequency. In our previous video also, I have said you about this cumulative frequency. Let us go with the cumulative frequency here.

[00:09:21]Let us take marks.

[00:09:27]Then students, or you can also write number of students.

[00:09:31]Okay, marks is x, students is f.

[00:09:37]Then we are going to see cumulative frequency. Yes or no? Then how much is the marks? Marks are 0 to 10, 10 to 20, 20 to 30, 30 to 40, 40 to 50.

[00:09:53]Number of students, how much it is? It is 3 8 12 7 2. 3 8 12 7 2. This is nothing special or I have not taken this values from anywhere.

[00:10:07]Whatever they have given in the question, that values only I have taken.

[00:10:10]Now let us find cumulative frequency.

[00:10:13]Cumulative frequency is nothing but in our previous video, I have said you that frequency, whatever the frequency is there, that frequency only you have to take here in the cumulative frequency.

[00:10:23]Then what you have to do? You have to add this cumulative frequency with the other frequency, then you will be getting the new cumulative frequency. 3 + 8, it is 11.

[00:10:35]11 + 12, it is 23.

[00:10:38]23 + 7, it is 30.

[00:10:43]30 + 2, it is 32. So this is our cumulative frequency. So we got 16th the term, right? We got 16th the term. So where this 16th the term lies, we have to see in the cumulative frequency. Do we have 16th the term or 16 number in this cumulative frequency? No, we don't have any 16th number. So what we are going to take? We are going to take the next number or the highest number after 16th. Highest number after 16th is 23.

[00:11:12]11 will be low, 30 will be more. So 23 is after 16th. So we are going to take 23 and which class interval lies in cumulative frequency 23? It is 20 to 30. So this 16th the term, you have to write like this, 16th the term lies between 20 to 30 class interval.

[00:11:43]Okay, so 16th term lies between 20 to 30 class interval. Now, we have to see what is the formula of median. Okay, let us see the formula of median, but before seeing the formula of median, first we have to know about L. What is L here? L is the lowest number in 20 to 30 in the class interval, whatever you are getting as the 16th term or the term which we have calculated, in which you have to see which is the lowest number. Is 20 lowest or 30 lowest? 20 is the lowest, so L here will be our 20.

[00:12:21]Next, we have to see cumulative frequency. Here, cumulative frequency we have seen as 23, but here, when we are taking cumulative frequency, we should not take 23. We should take the above number of it. What is the above number?

[00:12:35]It is 11. Then, we have to see interval.

[00:12:38]Interval is nothing but the gap between both these numbers. How much is the gap?

[00:12:43]The gap is 10.

[00:12:45]So, we are going to take 10 as the interval. What is the frequency?

[00:12:50]Frequency 20 to 30 is lying between which frequency? It is 12. So, F here will be 12. Let us see the formula now.

[00:12:58]The formula of median The formula of median is L plus n by 2 minus cumulative frequency by F frequency multiplied by I.

[00:13:18]Okay, so this is the formula. We need to substitute all these values into this formula.

[00:13:25]We will be doing the calculation here.

[00:13:28]Okay?

[00:13:34]Okay. So, we have seen L Let us again write the formula of median.

[00:13:44]L plus N by 2 minus cumulative frequency by frequency multiplied by I.

[00:13:55]How much is the L? L we have seen as 20.

[00:13:58]20 plus N by 2. How much is N by 2? N by 2 is nothing but the term. How much is the term? It is 16 minus cumulative frequency. What the cumulative frequency was? It was 11.

[00:14:12]11. Frequency. How much is the frequency? Frequency is 12.

[00:14:17]12 multiplied by I. How much is the interval? It is 10. Now you do the calculation. How much you are getting you see. Let me do the calculation. You also do the calculation.

[00:14:31]Okay, let me do here itself. 16 minus 11. How much it will be? 5. 5 by 12 into 10.

[00:14:44]20 plus 5 divided by 2. Mode let us do here.

[00:14:52]Now let us go with the mode. In the mode also same you will be taking marks.

[00:14:58]X Students or number of students you can mention. It is F. Yes, 0 to 10 10 to 20 20 to 30 30 to 40 40 to 50 And the students are three eight 12 seven to whatever they have given in the question, that thing only you have to take, okay? So, now here let us see the formula of mode, okay? We are having formula for mode also here in the continuous series. Formula is L plus F1 minus F0 by 2 F1 minus F0 minus F2 into or multiply by 1.

[00:15:52]This is the formula. Now, let us go with the formula. Substituting the values into the formula. L, how much it is? As we have seen when we were calculating mean, I said you that L is nothing but 20, least one. 20 plus F1. So, here you have to see 16th the term or the term which we have calculated in median was 20 to 30, lying between 20 to 30. So, here what is the frequency you see? It is 12.

[00:16:22]So, we will be taking 12. This 12 will be F1 and the above one will be F0 and the below one will be F2, okay? I think you are clear with this. Now, what we are going to do? 20 plus 12 F1 is So, when you do the calculation, our mode is something between 24.44, something like that. Okay, so mode here is 24.44.

[00:16:52]So, now we are done with mean, median, and mode. So, by watching both of these videos, you are perfect with the calculation of mean, median, and mode in both the series. If you are having any doubts, let me know in the comment section. For notes, you have to uh text me on my Instagram learn with Sahira, okay? See you all in the next video.

[00:17:12]Bye-bye.