 Hello. I welcome you all once again to my channel Explore Education. I am Dr. Rashmi Singh, assistant professor, department of education assistant at Gals-Rudi College, University of Allahabad. And I am discussing on nowadays topics over topics of statistics, statistics in education or educational statistics in which I have already discussed the concept of mean median and mode, that is measures of central tendency. And in this video, I am going to discuss how to calculate mean, that is computation of mean and computation of mean is very important and very relevant for all the students who have gone through statistics. Okay. So, we are going to talk about who we are going to talk about, we have to remove the map. Until now, we have to know that the map of central tendency in which the mother is the mother and the daughter-in-law and the mother is the mother. What I mean is that all the data is related to her, that is the point of the middle. The point of the middle is the median, that means the average. We have combined all of them, the amount and the amount of information that has been given to them, then our mother comes out. So, the mother is removed in two ways, either we will get ungrouped data or grouped data. So, ungrouped data is called means ungrouped data and ungrouped data. So, any data that has not been categorized in any way, is termed as an ungrouped data. For example, we have an individual who is 25 years old, another who is 30 years old, and yet another individual who is 50 years old. We have given that 3 individuals, 25 years old, 30 years old, 50 years old, we have not made any kind of ungrouped data. So, this is ungrouped data. This is independent picker. All of them are different from each other and not organized in any way. Thus, they are ungrouped data and this is ungrouped. What is grouped? Data that is categorized or organized is termed as group data. The category that we have organized is ungrouped data. Mainly, such data is organized in frequency distribution. Generally, we get this type of category in which we get ungrouped data. For example, we can have age range 26 to 30 years, 31 to 35 years, 36 to 40 years and so on. So, we will be told that in 26 to 30 years, we get ungrouped data. So, group data is convenient, especially when the data is large. When we have big eyes, then group data is convenient for us. Now, let's talk about ungrouped data. The formula for computing mean for ungrouped data is m is equal to summation of x upon n. Here, the sign of summation is not here, we will get it in the next slide. So, summation of x, that is, we have combined all of them. So, m is equal to mean summation of x is equal to sum of all these scores in the distribution. Suppose the scores are obtained by 10 students of psychology and as under. So what does 45 mean? It means that some children are more than 45, some children are less than 45, but overall average is 45. This is what Manthika or Ausat means. Everyone has taken it out, Ausat is very easy. Now we will come to the group data, which will seem a little typical to you. We also put Ausat in Maths. What do we do in group data? Group data, the formula for computing mean for group data is m. m is equal to summation of fx upon n. Summation means that whenever this sign is used, it is called summation yoga. It means that we have to combine all fx. And we have to run from n. What were we doing there? We were running from x to n. This was the difference in ungrouped data. What was in ungrouped data? Summation of fx upon n. What is f here? What is f? This is the frequency distribution, your respective frequency. Look at how many times it has come. This is the summation point. What is x? This is the midpoint of the distribution. What is f? The respective frequency is small f. How many times it comes out? And n is equal to total number of scores. There was also total number of scores. Now let's take it out. A class of 30 students were given psychology tests. They are categorized into 6 categories. They say that there are 30 students who have been tested for psychology. And they have got this number. In a psychology test, they have got the lowest marks obtained by 10 and the highest marks obtained by 35. That is, they have got the number from 10 to 35. A class interval of 5 was employed. The data is given as follows. Vargan Taral is 5. Now look at this. This is our Saroni. See, 10 to 14, 15 to 19, 20 to 24, 25 to 29, 45 to 49. This is not a Saroni. This is inclusive. It is not exclusive. So 10 to 15, 15 to 20, 20 to 25. This is an inclusive series. Now look at the frequency. There are 3 students in between 10 to 14. 15 to 19, 4, 6, 5, 7, 5. This is the frequency. Now we have to take out the midpoint. Because we don't know the actual score. We know that there are 3 students in between 10 to 14. So what is the midpoint of 10 to 14? 15 to 19 to 17. Or you can do it like this. Since this is Vargan Taral of 5, so the first 12 is 12, so 5 to 12 is 12. 5 to 17, 5 to 22, 5 to 22, 5 to 32, 5 to 35. You can take it out like this. You can take it out like this. Now what we will do is, we have to multiply all f by x. We have to multiply f into x. When there is no sign in between, this means that this sign is of the ring. From 5 to 37 we have to multiply it to 155. 254, 125, 132, 138, 136. We have taken out all fx. What we have to put in the formula is, summation of fx. So how much did we take out summation of fx? 780. And what is the frequency on n? We will put all this together. So what is the n? So the formula is, summation of fx upon n is equal to 26. This is the group data. This is the long method. Why is it long? It looks like a short method. It looks like a very long series. And since we have to multiply it again and again, from 5 to 37, 7 to 32, it looks like a very long series. That is why it is called a long method. It is a short method. And the group data is called a short cut method. If the question is asked, it will ask you. What is the short cut method? In certain cases, data is big large. It is possible that your data is very big. And it is not possible to compute each fx. So every time you multiply the midpoint from the beginning, it can be a little typical lengthy. In such situations, a short cut method with the help of a zoomed mean can be computed. So what is the short cut method? Let's assume one mean first. You can see something here. This can be the mean. Then what we will do? A real mean can thus be computed in the formula. And in this, we will add the zoomed mean. This is your correction. This can also be in the minus, or in the plus. You will know the actual mean. What is the formula? M is equal to zoomed mean. But we will improve it. Summation of fx dash. It should have been a dash. I didn't see its sign. Summation of fx dash upon Now what is am? The zoomed mean. You have assumed that this is the mean. Then the sign of the summation is i which is a class interval. What is x dash? This is the most important. What is x dash? x minus am upon i. x, midpoint, am, zoomed mean and i means we are running away from the variable. The midpoint of this course is a variable. F is the respective frequency of the midpoint. And what is the total number of frequencies or the students. Now we will apply this formula and you will understand. This is the same data. 10, 14, 15, 19, 20, 24, 25, 30, 34, 35, 40. This is the same frequency. The midpoint is the same. Now here we have seen how small the curve is. 15, 14, 5, 6, 9, 6. We have assumed 22. We thought we could have assumed 27. But we have assumed 22. So you have assumed 22. So this means we have to look at the result every time. So we have assumed 22. So we have to assume here. Where is it? Then as we go up, plus 1, plus 2, plus 3, plus 4, plus 5, plus 6. We will come down, minus 1, minus 2. There is no minus 3. You can see in the formula. X is the midpoint. This is zero. In 22, we will get 27. 5, 5, 1 is equal to 5. 5, 5 is equal to 1. Similarly, out of 22, out of 32, out of 32, 10, 10, 5 is equal to 2. We will keep this in the formula. And this is the same way. Wherever you take zero, 1, 2, 3, plus, minus 4, minus 5, wherever you go, this will be the formula. Now let's do the x-dash of f. What was f? X-dash is 3. So 5, 3, 15, 7, 2, 4, 5 is equal to 5. 6 is equal to 0. 4, 1, 4, 3, 2, 6. But we have to pay attention to the minus. This is not a game. It will go wrong. Then you should know that the root of the root is a root of the root. If the root is not a root, then the root is the root of the root. 15, 5, 20, and 34 are the root of the root. So this is summation of fx-dash is equal to 24. n is equal to 30. Now, in the formula, we have to add corrections in the sum. What is correction? Summation of fx-dash upon n into i Summation of fx-dash is n is equal to 30. So 30 is equal to 5. If you don't know the board mass and the rule of the board, you will do it wrong. You can do it like this too. If you do it before 34, then it won't be like this. First, it is given as a run. Then it is done. So, you will give the run of 24 to 34. So, 10-8 will be 8. If you do it before 10-8, then it will be 4. So, 4 is 4. How much was the previous method? It was 26. But it is less than here. So, this is a very small example. It has become very easy. It can also be a very big lengthy data. But you have to apply the formula every time. You have to pay attention to it. You have to pay attention to it. You have to pay attention to it. Then you will get the answer. And you have to pay attention to the concept. So, it is done. It is so easy. You have to learn media and more. You have to ask T-Test, ANOVA and COVA at the level of M&M. All right. I have done the computation of mean 2. So, thank you. And don't forget to like and subscribe my channel ExploreItVision. I have done from my side.