 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that 10 students in our test code marks in 3 different sections and they are given ranks in each section. In this session youth rank correlation coefficient to discuss which pair of sections have the nearest approach to marks and the rank distribution is given as the first rank which is denoted by R1 is given by 1, 3, 6, 4, 7, 9, 10, 2, 5 and 8. Second rank denoted by R2 is given by 2, 4, 7, 6, 8, 10, 9, 5, 3, 1 and the third rank denoted by R3 is given by 4, 2, 1, 5, 9, 8, 7, 10, 6, 3. We know that coefficient of rank correlation R is given by 1 minus 6 into summation of D square upon M into N square minus 1 where D is the difference between the corresponding ranks of 2 series and N is the number of individuals in each series. With this key idea let us proceed with the solution. We are given the following distribution of ranks. Now we shall find out the value of D12, D13 and D23. D12 is given by R1 minus R2 that is 1 minus 2 that is minus 1, 3 minus 4 is minus 1, 6 minus 7 that is minus 1, 4 minus 6 that is minus 2, 7 minus 8 is minus 1, 9 minus 10 is minus 1, 10 minus 9 is 1, 2 minus 5 is given by minus 3, 5 minus 3 is 2 and 8 minus 1 is given by 7. Similarly D13 is given by R1 minus R3 so we have 1 minus 4 that is minus 3, 3 minus 2 that is 1, 6 minus 1, 5, 4 minus 5 is minus 1, 7 minus 9 is minus 2, 9 minus 8 is equal to 1, 10 minus 7 is 3, 2 minus 10 is minus 8, 5 minus 6 is minus 1 and 8 minus 3 which is equal to 5 and D23 is given by R2 minus R3 that is 2 minus 4 that is minus 2, 4 minus 2 which is equal to 2, 7 minus 1 that is 6, 6 minus 5 is 1, 8 minus 9 is minus 1, 10 minus 8 is given by 2, 9 minus 7 is 2, 5 minus 10 is minus 5, 3 minus 6 is minus 3 and 1 minus 3 is equal to minus 2. Now, we can find out the values of D12 square, D13 square and D23 square. D12 square is given by minus 1 square that is 1, minus 1 square that is 1, minus 1 square which is equal to 1, minus 2 square which is equal to 4, minus 1 square that is 1, minus 1 square that is 1, 1 square which is 1, minus 3 square which is equal to 9, 2 square that is 4 and 7 square given by 49. D13 square is given by minus 3 square that is 9, 1 square that is 1, 5 square is 25, minus 1 square is 1, minus 2 square is 4, 1 square is 1, 3 square is 9, minus 8 square is 64, minus 1 square is 1 and 5 square is 25. D23 square is given by minus 2 square that is 4, 2 square that is 4, 6 square is 36, 1 square is 1, minus 1 square is 1, 2 square is 4, 2 square is 4, minus 5 square is 25, minus 3 square is 9 and minus 2 square that is 4. Now we should note that the value of summation of d1 to is equal to 0 which is equal to summation of d1 3 which is equal to summation of d2 3 also summation of d1 2 square is equal to summation of d1 3 square is equal to 140 and summation of d2 3 square is equal to 92 here the value of n is equal to 10. Now some of the key idea we know that rank correlation coefficient r is given by 1 minus 6 into summation of d square upon n into n square minus 1. Where d is the difference between the corresponding ranks of the two series and n is the number of individuals in each series. So we have r12 which is equal to 1 minus 6 into summation of d1 2 square upon n into n square minus 1 that is 10 into 10 square minus 1 which is given by 1 minus 6 into summation of d1 2 square that is 72 upon 10 into 10 square that is 100 minus 1 which is equal to 99. Therefore we have 1 minus 6 into 72 that is 432 upon 10 into 99 that is 990. On taking the ACM we get 990 minus 432 upon 990 which is equal to 0.5636. So the value of r12 is equal to 0.5636. Next we find out r13 which is given by 1 minus 6 into summation of d1 3 square upon n into n square minus 1 that is 10 into 10 square minus 1. So we have 1 minus 6 into summation of d1 3 square which is equal to 140 upon 10 into 10 square that is 100 minus 1 which is equal to 99. Therefore we have 1 minus 6 into 14 that is 84 by 99. On taking the ACM we get 99 minus 84 by 99 which is equal to 15 upon 99. Therefore we have 5 upon 43 which is equal to 0.1515. So the value of r13 is equal to 0.1515. Now we find out r23 which is equal to 1 minus 6 into summation of d23 square upon n into n square minus 1 that is 10 into 10 square minus 1 which is equal to 1 minus 6 into summation of d2 3 square which is equal to 92 upon 10 into 10 square minus 1 that is 100 minus 1 which is equal to 99. So we have 1 minus 92 into 3 that is 276 upon 5 into 99 which is equal to 495. On taking the ACM we get 495 minus 276 upon 495 which is equal to 219 upon 495 which gives 0.4424. So the value of r23 is equal to 0.4424. So we have r12 which is equal to 0.5636, r13 which is equal to 0.1515 and r23 which is equal to 0.4424. Since I have all the three values r12 is maximum. So we can conclude that the pair of first and second sections nearest approach to marks is complete file session. Hope you enjoyed this session.