 Hello, I welcome you all once again to my channel Explore Education, I am Dr. Rashmi Singh, Assistant Professor of the Department of Education, Assistant Nagar Street College, University of Allahabad. And this time I am going to discuss computation of media. We have already discussed how to compute mean for the grouped and ungrouped data and this time I am going to discuss how to compute media. Okay, so as usual the lecture will be in bilingual mode and it must be useful for all students who have to compute mean, median and mode for their numericals. So, first of all, we already know what is Madhika, we have read it, we have read its theory and we know that Madhika is a bindu which is equal to the scores above and below or it is Madhika bindu, Madhika, Madhika Ankar, right, like this. So, when there is more data, if we talk about ungrouped data then we will talk about group data. So, ungrouped data can be two ways or it can be odd number or even number, odd number i.e. 3, 5, 7, 9, 11, 13, 15, 17 will be your odd number and 2, 4, 6, 8, 10, 12, 14 will be your even number. So, if there is odd data then when the data is odd, the median is computed in the following manner. So, you can get the median like this. Look at the data, there are some marks like 8, 1, 34, 32, 37, 44, 36, 35, 34, 30. So, we have counted all of them. 1, 2, 3, 4, 5, 6, 7, 8, 9. So, n is equal to 9. So, first of all, we will not take out the median in such a way that we have seen what is the point of the median. We will first arrange it in ascending or descending order. We have already done this. First, the data is to be arranged in either ascending or descending order. i.e. if you have to arrange it in Aaruhi or Aaruhi Kramme. Okay. So, generally, we arrange it in Aaruhi Kramme. So, we will arrange the data in ascending order and it will look like this. If we keep it in a growing Kramme, we will see that the data looks this way. How can we start from the smallest? 32, 32, 34, 32 times. So, 34, 35, 40, 40, 41, 60, 61, 64, 70. If you had to remove the same data, then the 34 times would be 34. Anyway, we will talk about the mode later. So, we are removing the median. So, what is the formula? The following formula is then used to compute median. i.e. when for odd data, odd number, odd data means that vision number will be understood as many times as the angle is. So how are we going to remove it? md here, I wanted to write d but it didn't happen to me, next slide is fine. So md is equal to n plus 1 by 2th score. i.e. n, whatever is your n, what is your 9? So what will happen if we do 1 plus 1? If we do 10, if we do 2 then it will be 5. So 5th item, i.e. the average is 5. Which is the angle on the 5th? 1, 2, 3, 4, 5. Which is the angle on the 5th? This. So the average of this whole angle will be 35. Anyway, you don't have to do any computing in this. You can see that there are 4 angles above, 1, 2, 3, 4. There are 4 angles below, this is how it happened. So this is in the formula. As soon as you see it, you will have an idea. You will tell us the value of 35. Because 35 is 9. So 4 above, 4 below, 5 angles. Then you come for the VIN data. VIN data is even. The median is computing in the following manner. In this one more score is n is equal to 10 as well. 1, 2, 3, 4, 5, 6, 7, 8, 9. So what we are going to do is, we will arrange this data in either ascending or descending order. So we have started from 30, 30, 32, 34, 35, 39, 40, 48, 60, 64. So what will be the formula? The formula will be md. You will want to write this as ds. The median is equal to n by 2th score plus n by 2th score plus 1 by 2. What are you trying to say? You are trying to say that n by 2th score is 5th. That is 35. n by 2th score plus 1 is 6th. Because 5 plus 1 is 6th. And this is 49. So 35 plus 49 is equal to 27. So this md of ungrouped data will be md. You can understand it like this. When there is a problem. Sorry, there is a problem. So we will get the median point. 1, 2, 3, 4, 5. 1, 2, 3, 4, 5. There is no point in the median point. So what should we do? Combine these two and run away from it. Give 35 plus 49. What is this? Give 35 plus 49. So we can get the median point like this. If there is a problem, then take the middle point. Which is equal to the bottom point. And if there is a problem, then take the middle point. And then combine the two and run away from it. Take that. So this is the median point. This is easy. In the exam, we will generally ask you about group data. How to get the group data? The formula used for computation of median for group data is as follows. MD for median is equal to L plus. We have to give two things. First, we should remember the formula. Second, we should know what is L in the formula. What is F? What is capital F? What is small FM? What is I? What is N? And we should be able to correct the question. You can do a small numerical. If you know the table, then there is no problem. Generally, students are very afraid of statistics. Especially, R-psychologists, who give MMA education, or in sociology, who give economics to those children. Economics people have to apply a very mathematical formula. So don't worry. This is very easy. Look, MD is equal to L plus. If we studied in Hindi in childhood, it was said that it was a big coast, that it was a small coast, that it was made like this in between. It was a rough coast. But let's talk to you like this. Square bracket, right? Then why is it necessary to apply this big bracket? Because even after this, there are more marks. There are more marks. You have to keep an eye on the formula. Otherwise, it would have been just N by 2. So it would have worked only with a small coast. So L plus N by 2 minus F upon FM. That is, we have to remove F upon FM. We have to remove it from N by 2. And whatever it has to do with I, and we have to combine all this ink. Now look, what is all this? MD is equal to median. What is L? L is equal to lower limit of the median class. Because it is a group data. There will be a class interval. There will be a frequency. Sorry. So the median you will get in the class interval, means the class interval in which there will be a median, it will be called the median class. So the lower limit of that class, the lower limit of that class is L. What is N? Total of all the frequencies. We always have N in statistics. What is N? It is made from N. It is made from N. So the whole number is N. So N is equal to total of all the frequencies. What is capital F? Sum of frequencies before the median class. That is, you are going up. As you will know in the next slide. So the median class in which the class interval will be, its lower, sorry, lower limit of the class is L. If you look at the example, you will understand. Sum of frequencies before the median class. The frequencies before the median class, we have combined them. So our capital F is here. What is small FM? Frequency within the interval upon which the median falls. Your falls. Frequency within the interval. We need the interval above which the median falls. If you look at it, you will understand. What is the class interval? I will tell you the entire class interval. Look ahead. This is the formula. This is the formula. 10 to 14, 15 to 19, 20 to 24, 25 to 23, 30 to 34, 30 to 30. Frequency is given to all. 3, 4, 6, 5, 7, 5. We combined all of them. So we got 1 data here. N is equal to 30. What is the class interval? 10 to 14, 5 to 11, 11, 12, 13, 14. So I is equal to 5 and N is equal to 30. We got two things here, which we have to keep in the formula. We will have to take them out. How will we take them out? First of all, what is the formula? The formula was your N by 2. So first of all, what do we have to take out? We have to take out N by 2. So what will be N by 2? The first step is to compute N by 2. That is 30. We combined N. How much did we get? We got 30. So N is equal to N by 2. So that is 30 by 2. So that we obtained 1 half of the scores in the data, 15 in this case. That is, N by 2 means 32. 32 means 15. So in this case, we got 15 N by 2. Okay. Then it says, scores are even in number. 30, right? The score is 30. So what will be our formula? 15 plus 16. It should not be 2. 15, 15 and 16. It should be somewhere in between. Right? So where are the 15 and 16 scores? Look at this. Right? This frequency is 3. It has 4, 7. And it has 6, 13. Let's go from the top. It has 5, 7, 12. And it has 5, 17. This means that it has 13, 17. And it should be between 15 and 16. This means that we can consider this class to be medium class. Why? How did we understand it? How did we understand it? N is equal to 30. 30 by 2 is equal to 15. So 15 is our event. It is 30. It is an event number. So what will we do with this? It will be somewhere between 15 and 16. So we don't know the score. It is 3, 4, 6. So these are all connected. 3, 4, 7, 6, 13. If we connect from the top, then 5, 7, 12 and 5, 17. So it will be in the 13th class. In which class? It can be in the 17th class. Because it should not be in the 24th class. 15, 16, 17. It is around this. So in the 17th class, for our convenience, we accepted that this is medium class. It is 25 to 29. Okay? This is how it starts later. You don't have to take it out. Look, it is almost 40. So this is 20 to 24 or 25 to 29. None of these can be a medium class. Neither it will be 15 or 19, nor it will be 10, nor it will be 30 or 30. So you can take this. You can take this. We have taken this. So from 25 to 29, we have taken a medium class. So what we wanted was the lower limit of the medium class. That is, it is starting from 25. So the lower limit of it is always that it is less than 10 to 5. That is, 24 to 10 to 5. If we talk about the upper limit, then it must be 29 to 10 to 5. Why? Because it is 30 here. Do you understand? So these are all assumptions. We accept them the same way. We do it the same way. So it is 25. So the lower limit of 25 is 24 to 10 to 5. So we will find out how many things are there. Look, as this score is our evening number, the median should fall between 15 and 16 score. Whether we add the frequencies from above, if it is from above, then it is 17, then it is said that the median will definitely fall between 25 and 19. Then it will fall between 25 and 19 and the lower limit will fall between 24 and 19. Now what we wanted to do? What we wanted to do? Look at this question. We also found out L from 24 to 5. We also found N by 2 from 15. What was capital F? Some of the frequencies before the median class. The intermediate class of the median class has to be connected to all the frequencies below. So what happened to the median class? It will fall between 25 and 19. That is, how many frequencies below? 4, 3, 6, 3, 13. So we also found out capital F. We found out capital F. Now what we want to do? We want to find out a small fm. It is a frequency within the interval upon which the median falls. Falls. In the present example, the median class interval is 25 to 29 and the frequency for this class interval is 500 fm is equal to 5. That means the class interval you have taken as the median class is the average fm. Look at this. It is written here. fm is equal to frequency within the interval upon which the median falls. The time in the present example the frequency for which the median falls is coming is the average fm. So look at this. We have taken the median class from 25 to 29. The average fm is 5. Now we know everything in the formula. What was our formula? The formula was median is equal to L plus n by 2 minus capital F upon small fm into I. Md median L was the lower limit of the median class. We have taken the median class from 25 to 29. The lower limit was 24 to 25. We have come to know n by 2 n is equal to 15. The class in which the median class falls is the average fm. The class in which the median class falls is 5. We have come to know everything in the formula. Look at this. This is formula Md is equal to L plus n by 2 minus capital F upon small fm into I. The bracket will be out of the bracket. Not that we will mix everything together. All these big brackets and all these big brackets and all these big brackets and all these big brackets are out of the bracket. Now we will come to know the number of brackets that the bracket is equal to 15. But there is a big bracket called b By 14 So, 10 upon 5 is equal to 2. So, 24.5 plus 2 is equal to 26.5. So, for this grouped data, your Madhika command is 26.5. And it falls in the median class interval 25. Say 29. I mean, we knew that somewhere between 25 and 29, but we didn't know exactly. So, we knew that 24.5 is the median class interval. Meaning, above 24.5 and below 24.5, all the values are equal. Okay? So, the meaning of this is that it's easy to predict, but the concept is already clear. What is the median class interval? Then, we need to remember the formula that median is equal to L plus N by 2 minus capital F upon F into I. There's a small calculation. So, we need to remember the formula. N is equal to 30. 30 divided by 2 is equal to 15. The first median class is equal to its lower limit. So, we need to remember 25. So, we need to remember 24.5. Then, all the frequencies of the lower class are equal to capital F. Then, the median class is equal to Fm. So, between 10 and 14, the median class is equal to 5. So, we don't need to remember the formula. We need to remember 10 to 14, which is spontaneous. So, 24 divided by 5 is equal to 15 minus 13 divided by 5. Now, it doesn't seem like 15 minus 13 divided by 5 is equal to 13 divided by 5. The old saying is wrong. No. First, we need to divide this. So, the one that divides is equal to 15 divided by 13. This can also be the case that this is very much in minus. And this can also be the case in this. So, we need to remember the plus and minus. So, you need to have a basic mathematical ability. Whenever you have learned math in your childhood, you should have a clear concept in your mind. And if you don't, then learn it now. But, learn it now. Because, if you don't want to do it, and if you don't want to run away from it, then it's a very easy way. So, who likes an easy way? Choose a difficult way. Then, when you see how happy you will be when you will be able to ask questions. Okay. So, in this way, we have learned how to compute median for the grouped as well as ungrouped data. If you have an event in ungrouped data, then you have to divide between the two. If you have an odd, then you will be able to get the same amount of data. You can also do it without the formula. But, if you want to keep it in the formula, and if you have grouped data, then you should know the frequency. What is the lower limit? How do you do it? Write it in the right formula. Take out the median. So, we have learned how to take out the mark and we have also learned how to take out the mark. Now, your central tendency is mode. Okay. So, next time, we will talk about how to take it out. So, I have completed this very topic too. So, thank you all, and don't forget to like and subscribe my channel Explore Education. I have done it from my side.