 Hello, I welcome you all once again to my channel Explore Education, I am Dr. Rashmi Singh, Assistant Professor, Department of Education, and I have already discussed with you the concept of quartile deviation and standard deviation and in this video I am going to discuss how to compute quartile deviation for ungrouped and grouped data. So the lecture in bilingual mode and it must be useful for your various competitive teaching examinations as well as for your subjective B.A.M.A and B.A.D.M.A papers. So first of all, for grouped data, one minute, for grouped data, from the grouped data quartile deviation can be computed by the formula. We are saying that when we get a vulgic chart, then how will we get the chart from Chaturthaan-Shwichalan and how will we get this chart from Chaturthaan-Shwichalan. So we have discussed with you that Q is equal to Q3, i.e. the 75th place, the 25th place, we will remove it and we will run away from it. It is also called semi-interquartile range, which is called Q3 minus Q1, it is called interquartile range. So if we know Q1 and Q3, then we will get to know Q. Why? Because Q3 has to be removed from Q1 and run away from Q2. Now the formula for Q1 is this and the formula for Q3 is this. If you remember the formula for median, then this is different from that. Q1 is equal to L plus, where is this person? Q1 is equal to L plus i, it is in the bracket N upon 4. Because we have to remove Q1, Q1 is the 25th place, right? Because we have divided the whole data into 4 parts, 25%, 25%, 25%, and 25%. So the first 25, that is why we have taken n by 4 minus come fi, this is the cumulative frequency of your upon FQ. Similarly, when we remove Q3, the whole formula will remain the same. Since we have to remove the 25th, then we will do 3n by 4. This was 1n by 4. When we remove Q2, then 2n by 4 will come. This means n by 2 is the formula for median. And if we remove Q3, then it will be 3n by 4. You can see that this is the formula for median. So Q1 is equal to L plus i, N upon 4 minus cumulative frequency upon FQ. Q3 is equal to L plus i, 3n by 4 minus cumulative frequency upon FQ. So where L is equal to the exact lower limit of the interval in which the quartile falls. That is, the time in which your quartile will come, the exact lower limit. We need a lower limit for that. We know that if 10 to 20 is like this, then 9 to 10 is 5 in the lower limit. If it is 29 to 30, then 19 to 10 is 5. Then what is i? The length of the interval. The length of the interval. The length of the interval is i. It is L which we got the lower limit. The length of the interval is L. The length of the interval is i. What is N? The total number of observations. I have always said that there will always be total number of observations. And what is the term FI? The cumulative frequency up to the interval which contains the quartile. That is, the time in which the quartile is coming, please leave the room. The time in which the quartile is coming, up to the first time, we get the cumulative frequency. Now you will see in the next table how the cumulative frequency is removed. And FQ, the F on the interval containing the quartile. That is, what is the frequency of the quartile in which the quartile is coming? It is FQ. The cumulative frequency up to the first time is the term FI. The length of the interval is i. The length of the interval is L. The lower limit of the interval is L. And this is the formula. Please remove Q1 from this. Remove Q3 from this. Stop it. Remove Q1. Remove Q3. And then Q will come. If we get to know the value of Q3, Q1, then the value of Q will come. Obviously it will come. Why? Q3 minus Q1 upon 2. That's it. Then, sorry. This slide should have been there. No problem. First let's look at the ungrouped data. Let's look at the formula of the group data. Let's look at the example of the group data. Let's look at the example of it first. Then we will look at the ungrouped data. We were talking about the group data. So, this is the group data. Let's return to the ungrouped data later. Where is group data? Look. It was 144 Ah, 145 Ah, 149 Ah, 159 Ah. 154 Ah, 155 Ah, 159 Ah. Let's say it is 155 Ah, 159 Ah, 159 Ah. These are the ungrouped data. These are the ungrouped data. Let's do it like this. The cumulative frequency, meaning how to extract the ungrouped data? We will connect them. If there are 1, then we will have only one, because there is nothing to connect to. One form of 3, we get 4 2 plus 2 is 6. 4 in 6 is 10. 10 is 4, 14 is 6, 20 is 20, 10 is 30, 8 is 38, 35 is 40, 40 is 40, 40 is 40, 20 is 50. So, you also know that n is equal to 50 and you also know the cumulative frequency according to the number. Now, in the formula, what is 1 is equal to L plus I, n upon 4 minus come FI upon FQ. So, what is this? n is 50, right? n is 50 and 50 is 12, 10 is 5. So, we will have to see where 12, 10, 5 is coming. So, see where 12, 10, 5 is coming. It will come in this. This is 10, that is 12, 10, 5 will come in this, right? This is 10, that is 10, this is 14. So, 12, 10, 5 means this one is the range of our quartile, 160, 166, and what we want is lower limit. So, if this is a 160 issue, then what is the lower limit? 159.5. So, what is L in the next formula? What is 159.5? So, what is I? So, what is I? FI is equal to 10, cumulative scores up to interval containing FQ is equal to 4. See, what is your FQ? Its FQ is 4. What is its frequency? 4. So, you know FQ. What is CMFQ? 10. So, what is your FQ? It comes in this. This is 159.5. So, how do you say 4? FQ is 10, from the top of the screen. What is FQ? So, we have 5, we have 5. So, that is 159.5 for me. So, what is this FQ? So, what is FQ? 159.5 for me. So, we have 159.5 for me. So, we have 159.5 for me. So, FQ is 159.5 for me. So, 159.5, 159.5 for me. So, we have 159.5 for me. 159.5, your L is L, I is 5, N is 12.5, F is less than F, I is 10, B is 4, so your answer is 162.6. So Q1 value is 162.62, similarly Q3, what will happen? Just this 3, it will be 3, L plus I into 3, N upon 4, minus less than F, I, F I should be F I, this is F L, sorry. Then FQ, 3 upon 4, N is equal to, so just take it out, everyone knows, it's just 3N here, here N upon 4 was 12.5, so it will be 3 to 5, 12 to 5 to 3, so it will be 5 to 7, it's all the same. Okay, Sanjayatma Kabriti will change, right? Okay, one second, one thing left to tell, because please close the door and go, 3N upon 4, so 3N upon 4, 37.5, so we will have to see which 37.5 is coming, so 37.5 is coming in this, next, this is 30, so this time our quartile class interval will change, it's starting from 175, so our minimum limit will be 174.5, so this is your, this is 174.5, this will change, oh, it will change, sorry, sorry, I told you a little bit wrong, I mean, here, I mean, in the formula, it's 3N upon 4, but from this, we will get to know which one has to take the width, the width, the interval, which one has to take, we got to know from 12.5 that it has to take 160, it's going from 37.5 that it has to take 175, it's going to take 179. If you don't know, then you can easily take it out, how will it come out? This is the Q1 from Q3, and the amount that is coming, let it run from 2, so 8, 10, 2, 8 has come, thus the quartile deviation for the above data is 8.28. This is what is going on, grouped data, when you get a vargikrit mark, now let's talk about a vargikrit mark, when you get it, the formula will be the same, Q3 minus Q1 upon 2, where Q1 and Q3 are the first and the third quartiles of the data, we got to know, and that is why we are saying that the second quartile is not the same media, right? And you can also get the coefficient of quartile deviation, see, all these formulas and all these things are very easy to do for your competitive examination, why? Because you have to do a small calculation, Q1 will give you, Q3 will give you, if you ask for quartile deviation, then the formula will be Q3 minus Q1 upon 2. If you ask for the coefficient of quartile deviation, then the formula should know that Q3 minus Q1 upon Q3 plus Q1, and you can get it out. So how will you get it out? You have to believe that this is the amount that is given to the obtains, so what will you do? First, you put the data in ascending order, in increasing order, so you have put it in 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, this is the data, so how does Q1 get out? N plus 1 by 4th position, so this is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11 is equal to 11, so 11 plus 1, i.e. 12, 12, 24, i.e. the third position, what does it mean? 1, 2, 3, the third position is 25, so what will be the first quartile? 25. Similarly, you take out Q3, Q3 has the same formula, so it will be 3 into N plus 1 upon 4, because it has to be 3 times, i.e. the third position, so N plus 1 by 4th, so what is it? 11 plus 1, 12, 12, 12, 4, i.e. 3, so it has to be 3 times 3, i.e. the ninth position. So, what is the ninth position? 1, 2, 3, 4, 5, 6, 7, 8, 9, 11 is equal to 34. So, this is your Q1 and Q3, don't get confused. When Q1 and Q3 get out, the work is over. When Q3 gets out, Q1 will get rid of Q3 and run away from Q1. So, Q3 minus Q1 upon 2, Q3 is 34, Q1 is 25, Q3 minus Q3 is 25, and 9 is equal to 4.5. This is how you will take out ungrouped data, because you have to arrange it in ascending order. Look, you have to understand that you always have to do this. On the fourth position, N by 4th or 3N by 4th. This is what you have to take out. But since it is VAR-Gantaral, that is why you have lower limit, VAR-Gantaral, cumulative frequency, its frequency, you have to combine all these formulas. The other way is this. So, this slide should have been first, and then this slide should have been for group data. Then this will go like this. For ungrouped data, N plus 1 by 4th position is Q1, and 3N by 3 into N plus 1 by 4th position is Q3. So, Q3 minus Q1 upon 2 is equal to QB, quartile deviation. For this, the formula is Q3 minus Q1 upon 2. But Q1 minus L1L plus I into N upon 4 minus cumulative frequency upon frequency of that very class interval. And Q3 is equal to L plus I into N by 4 instead of 3N by 4. And as soon as it becomes 3N by 4, your VAR-Gantaral will change. So, the cumulative frequency and frequency will change, and lower limit will change. I will remain the same. Okay. So, in this way, we can take out quartile deviation for group data and for ungrouped data. So, you have to remember the formula, Q3 minus Q1 upon 2. This is important. And it is very important. And now, the coefficient of quartile deviation Q3 minus Q1 upon Q3 plus Q1. So, the formula should be known. The concept should be known. Then you are right. Q median is Q2. Why? Because the median is 50th position. And we divided it into 25, 50, 75, 70. So, Q2 is equal to median. Okay. So, in this way, I have completed how to compute quartile deviation for ungrouped and grouped data. So, thank you. And don't forget to like and subscribe my channel Explore Education. I have done from my side.