 Hello and welcome to the session. In this session we are going to discuss the following question which says that the following table gives the record of the height of 9 athletes and the measurements of their long jumps calculate their ranks and coefficient of correlation of ranks We know that rank correlation coefficient r is given by 1 minus 6 into summation 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. With this key idea let us proceed with the solution We are given the following data Here the height of the 9 athletes are given as 159, 162, 160, 165, 163, 169, 177, 174, 170 and the measurement of their long jump is given as 300, 310, 325, 315, 321, 400, 350, 413 and 375 Now we need to find out their ranks When ranks are not given but actual data are given then we should assign ranks that is we can give ranks by taking the highest or the lowest as 1 next to the highest or lowest as 2 and follow the same procedure for both the variables Here we take the highest as 1 and next to the highest as 2 and follow the same procedure for both the variables ranks in x is denoted by r1 and ranks in y is denoted by r2 since the highest height is 177 centimeters therefore rank 1 is assigned to it and the lowest height is 159 centimeters therefore rank 9 is assigned to it Similarly the highest measurement of the long jump is 413 centimeters and the lowest measure is 320 meters with their respective ranks as 1 and 9 Now we shall find out the difference of the 2 ranks and the square of their difference D is given by r1 minus r2 that is 9 minus 9 which is equal to 0, 7 minus 8 minus 1, 8 minus 5 is 3, 5 minus 7 is minus 2, 6 minus 6, 0, 4 minus 2, 2, 1 minus 4, minus 3, 2 minus 1 that is 1, 3 minus 3, 0 and D square is given by 0 square that is 0 minus 1 square that is 1, 3 square that is 9, minus 2 square given by 4, 0 square, 0, 2 square, 4, minus 3 square that is 9, 1 square, 1 and 0 square which is 0 Also we have summation of D square that is sum of all the elements in D square is given by 28 and we know that rank correlation coefficient as is equal to 1 minus 6 into summation D square upon N into N square minus 1 Where D is the difference between the corresponding ranks of the 2 series and N is the number of individuals in each series Here the value of N is equal to 9 and rank correlation coefficient R is equal to 1 minus 6 into summation D square upon N into N square minus 1 which is equal to 1 minus 6 into summation D square is 28 upon N is 9 that is 9 into 9 square minus 1 which is equal to 1 minus 6 into 28 upon 9 into 81 minus 1 that is 1 minus 6 into 28 upon 9 into 80 which is given by 1 minus 7 by 30 on taking the LCM we get 30 minus 7 by 30 which is equal to 23 by 30 that is approximately equal to 0.77 So R is given by 0.77 therefore rank correlation coefficient R is equal to 0.77 which is the required answer This completes our session hope you enjoyed this session