 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says, from the data given below, state which group is more variable A or B. So this is the table given to us. In the first row, we have marks, intervals are 10 to 20, 20 to 30, 30 to 40 and so on, till 70 to 80. In the second row, we have the data for group A. In the third row, we have the data for group B. So what we do in this question is, first of all, we find the variance for group A, then we find out the variance for group B and then we compare both of them. So let us start with the solution to this question. We make a table like this. First of all, for the group A. Now, let us see how to find the variance. Step one is, obtain the midpoint of each given class interval, that is xi. xi is equal to upper limit plus lower limit divided by 2, then choose a convenient number A, usually the middle or nearly middle of xi's, which we call as assumed mean, that is A denotes the assumed mean. Step two is, find yi that is equal to xi minus a divided by h, where h is the difference between any two consecutive xi's and step three is finally finding out the variance that is sigma square is equal to h square divided by summation fi, where i goes from 1 to n the whole square, multiplied by summation fi, i goes from 1 to n into summation i goes from 1 to n fi yi square minus summation fi yi, where i goes from 1 to n the whole square. So this is the formula of variance. Now, this is how we find out the variance, first of all for group A, then for group B and then we compare both of them. In order to find out the variance of group A, first thing that we have to do is we obtain the midpoint of each given class interval, that is xi, that is equal to upper limit plus lower limit divided by 2. So, x1 will be, now upper limit is 20, lower limit is 10. So, we will have 20 plus 10 divided by 2, that is equal to 15. Similarly, we find out x2, that will be 30 plus 20 divided by 2 and that is equal to 25. Similarly, we find out x3, x4, x5, x6 and x7, just write down the xi's in the second column. For this class interval it is 15, for this it is 25, 35, 45 and 75. The fi's for group A, the fi's were 9, 17, 32 and so on, for the groups 10 to 20, 20 to 30, 30 to 40 and so on respectively. So, we just write down here, fi's that are 9, 17, 32, 33, 40, 10 and 9. Now, we sum up fi's and that comes out to be 150. Now, we choose a convenient number capital A, usually the middle or nearly middle of xi's. The difference between any two consecutive xi's, so we have 25 minus 25, 35 minus 25 is equal to 45 minus 35 and so on, is equal to 10, zoomed mean divided by h, to mean divided by h. So, for the first interval, we will have interval yi will be minus 45 divided by 10 and that is, for this it is minus 1, 0, 1, 2, 3. So, these are yi's for different yi, fi will be 9 into minus 3 is minus 27. So, this is minus 27, 7 into minus 2 is minus 34, into minus 1 is minus 32, 33 into 0 is 0, here we will have 40, 10 into 2 is 20. So, the yi, so these are the yi's, simply multiply this with this and 81, these are fi, yi's squares for these respective intervals and 42. Find out the variance that is h here and we get the variance for group A. So, this is the formula for the variance, now we simply put in the values here, since h was equal to 10, so h square would be 100 divided by, now summation of fi's was 150, 100 divided by 150, the whole square, multiplied by, again, summation fi was 150, multiplied by summation of fi yi square, summation of fi yi square is 342. So, this gets multiplied by 342 minus summation of fi yi whole square and before the written as 100 divided by 00, multiplied by 2 is 51300 minus square of minus 6 is 36, 5 multiplied by 100, this is 51264, with 100 we have 5 and that gives us 227.84, 7.84, therefore, equally equal to 15.09. Now, the variance, group B, that will be 10 plus 20 divided by 2 is 15, 20 plus 30 divided by 2 is 25 and so on, 70 plus 80 divided by 2 is 75. Now, let us write down the fi's, that is frequencies for the group B, that is given to us in the question as 25, now the summation of fi's, that is 150. Now, we have to find that we divided by h, take assumed mean to be equal to 45 and we can see that h is equal to 25 minus 15 is equal to 35 minus 25 and so on, we have 10. So, now let us calculate yi to 20, yi will be minus 45 divided by 10 and that is minus 3, for next we have minus 2, minus 1, 0, 1, multiplying this by this, here we will have minus 30, minus 40, minus 30, 0, 43 ones are 43, 15 twos are 30, 7 threes are 21. Now, the next thing that we find is yi of 9, where will be fi multiplied by yi square, that is 10 into 9 is 90, 20 into 4 is 80, 30 into 1 is 30, 25 into 0 is 0, 43 into 1 is 43, 15 is 63. Now, we sum up yi fi's and fi yi square, we see that this sums up to 366 can be found out by this formula. So, let us write this formula here, we have will be 100. Now, summation of fi, summation of fi's is 150 multiplied by summation of fi yi square, summations of fi yi, that is minus 6, we have 1 divided by 225 multiplied by 615, this is approximately equal to variation. So, first of all we calculate the coefficient of variation for group A, A we see that the coefficient of variation is equal to sigma divided by 200, standard deviation and this is the mean of the distribution multiplied by 100. Now, we have seen 45 multiplied by 100, approximately. So, coefficient of variation for group A is 33.53 is for group B. For group B, coefficient of variation would be again standard deviation divided by mean multiplied by 100, variation for group A is this and for group B is this. So, we can clearly see that coefficient of variation, the question and enjoy the session. Have a good day.