MEAN/MEDIAN/MODE PART-1 | Degree semester-2 Business Statistics UNIT-2 explanation part-1

[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 discrete series. Discrete series is also known as ungrouped data. I'm going to upload two videos, part one and part two. The video which you are watching now is part one in which we are going to see the calculation of mean, median, mode in discrete series or ungrouped data. In the other part, in part two, in the other video, we are going to see the calculation of mean, median, and mode in continuous series, which is also known as grouped data. So, if you watch both these videos, part one and part two, you will be perfect with calculation of mean, median, and mode in both the 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're watching this video, you have to watch this video till end and definitely you have to watch my part two video also, so that you will be perfect with this topic. Okay. And 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.

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[00:01:43]So, without getting late, let us get started with our discrete series calculation of mean, median, and mode.

[00:01:50]First, we will be calculating mean, then we will be going with median, in the last we will be seeing mode. Okay? So, first let us calculate mean. To calculate mean, first we have to take income and frequencies. Whatever they have given in the question, that thing only you have to put in put in your answer also. So, first one is income.

[00:02:10]Take income. Income they have denoted as X. If they don't give X in the question also, you should assume income as X, okay? Definitely, if they give X and F, that is completely okay and fine. If they don't give X and up F, you have to assume income as X and the other one whatever they give as F. So, draw a box.

[00:02:36]Then second one is frequency.

[00:02:41]Frequency is F.

[00:02:44]Okay.

[00:02:46]Now, whatever they have given in the question, that only you have to copy paste.

[00:02:51]10 12 14 16 20 Then frequency it is given as five eight 15 seven five.

[00:03:06]Okay. So, this is what they have given in the question. After taking X and F, next we are going to see FX. FX is nothing but when you multiply X value with F value, you will be getting FX, okay? 10 into five, whatever the value will be, that is FX. 12 into eight, whatever the value will be, that will be FX, okay? So, don't do any mistakes. You just take a calculator and calculate so that there will be no mistakes, okay? 10 into five, how much it is? It is 50. 50 is our FX.

[00:03:40]12 into eight 96 is our FX.

[00:03:45]Then 14 into 15 210 16 into 7 112 20 into 5 100 Okay, so this is our FX. After finding FX, we have to see sigma FX. Sigma FX is nothing but when you add all the values of FX, you will be getting sigma FX.

[00:04:15]Okay, so add all the values. 50 plus 96 plus 210 plus 112 plus 100. How much it is? It is 568.

[00:04:26]Okay, then we have to know N also. This is known as N or we can also call it as sigma F. Your wish, whatever you want to call it, you can. Okay, 5 plus 8 plus 15 plus 7 plus 5. How much it is? It is 40.

[00:04:44]When we add all these values, we will be getting sigma FX. When we add all these values of frequency, we will be getting N or sigma F. Okay, so after getting this sigma FX, let me just highlight it with red pen.

[00:04:59]You can take any other pen, okay? But other color pen. Okay, so we are going to see the mean.

[00:05:07]So in your examination also, in your answer booklet also, you have to draw this box, okay? I'm using pen itself, but you have to use pencil and scale and you have to draw this box neatly. So to find mean, we should know the formula of mean. Formula of mean is nothing but X bar equals to sigma FX by N. This is our formula. We need to substitute all the values into this formula. Okay.

[00:05:38]X bar equals to FX, how much it is? It is 568.

[00:05:43]And N, how much it is? It is 40.

[00:05:46]Now you calculate this.

[00:05:49]568 / 40. How much it is? It is 14.2.

[00:05:56]Okay? So, here mean is 14.2. You can write like this. Okay, we have calculated the mean, we got the mean. Now, let us go with the median.

[00:06:14]Okay. So, let us see the formula of median. If you know the formula, then only you will be able to do the mean median. So, first we need to understand the formula. Okay, what is the formula of median? It is n + 1 / 2 the term.

[00:06:33]Or we can also say it as item. Okay, we can say it as term or item. Your wish.

[00:06:38]So, to find median, first we should know cumulative frequency. Okay? To find median, we need to know cumulative frequency.

[00:06:49]Let us find cumulative frequency. What is cumulative frequency? Let me say you all. Cumulative frequency is nothing but see, first frequency, whatever it is there, you have to take it as it is.

[00:07:00]Okay, here we have five, that is why we are taking five. If we have 10 here, we have to take 10. If we have 15 here, we have to take 15. So, whatever the first frequency is there, you have to take it like that. Then, you have to add this cumulative frequency with the other frequency. Then, you will be getting the new cumulative frequency. Okay, let us add 5 + 8.

[00:07:23]How much it is? It is 13. Then, you have to add 13 + 15. You will be getting the new cumulative frequency. 13 + 15. How much it is? It is 28.

[00:07:35]28 + 7. It is 35.

[00:07:40]35 + 5. it is 40.

[00:07:44]So, this is our cumulative frequency.

[00:07:46]When we When we get the cumulative frequency, we can go with the median.

[00:07:51]Okay, so let us substitute the values into this formula. What is n?

[00:07:56]n is 40 plus one by two the term.

[00:08:03]Okay.

[00:08:06]Let us do the calculation now. See, 40 plus one by two the term. Now, let us go with the calculation part.

[00:08:16]So, what it is?

[00:08:20]40 plus one by two means 41 by two.

[00:08:23]Okay, we have to do 41 by two.

[00:08:29]41 by two the term.

[00:08:37]Do the calculation, what you will get?

[00:08:40]41 divided by two.

[00:08:42]It is 20.5.

[00:08:46]So, here 20.5 is the term.

[00:08:53]Oh, okay.

[00:08:54]20.5 the term. Now, we have to see this term or this value in our cumulative frequency. If we have this value in cumulative frequency, then okay. If we don't have, what we have to do? Let me say you.

[00:09:08]Okay, so see here in the cumulative frequency, do we have 20.5? No, we don't have 20.5. So, what we are going to do?

[00:09:16]We are going to take the next number after 20.5.

[00:09:21]13 will be less, 35 will be less, but 25 28 is after 20.5, right? But less than 28, nothing is there. It should be highest or it should be the next number after 20.5.

[00:09:36]So, it is 28. So, here this is the cumulative frequency. For this, what is x? You have to see. Here it is 14. Okay, x is 14. So, 14 is nothing but our median. What is 14? 14 is our median.

[00:09:54]So, we have to write therefore median is 14.

[00:10:04]Okay, we got the median. Now, let us go with mode.

[00:10:09]Mode is also known as z. Okay, what is mode? Mode is nothing but highest frequency. Okay, what is highest frequency? Means what is the big number in this frequencies? You have a look. 5 8 15 7 5. What is the highest frequency here? It is 15. Yes or no? This is the highest frequency. So, what is there with these frequency? What is in the x column? It is 14. So, here 14 will be our mode.

[00:10:43]14 will be our mode. So, therefore mode is 14. Okay? So, this is what it is the calculation of mean, median, and mode in discrete series. For the calculation of mean, median, mode in continuous series or grouped data, you have to watch my other video which is part two. And don't forget to subscribe our channel Learn with Sahira for more videos and for notes of all the subjects and languages, you can text me on my Instagram. See you all in the next video. Bye-bye.