 Hello and welcome to the session. In this session we are going to discuss the following question which says that 10 competitors in a dance competition are ranked by two judges in the following order. Find Kindle's coefficient of rank correlation. We know that Kindle's coefficient of rank correlation denoted by tau is given by total score by maximum possible score. Here total score is denoted by S by maximum possible score which is equal to Nc2 that is S upon N into N minus 1 by 2 which is equal to 2S upon N into N minus 1. Where N is the number of pairs of observations C2 is the number of all possible combinations of the pairs of N observations. With this key idea let us proceed with the solution. Here rank given to the 10 competitors by the first judge is as follows 2, 1, 6, 7, 4, 3, 9, 10, 8, 5. And the corresponding ranks given by the second judge to the 10 competitors is as follows 6, 4, 3, 2, 7, 5, 8, 9, 10, 1. Now we first rewrite the ranks assigned to the 10 competitors by the first judge in ascending order and represent the corresponding competitors by A, B, C, D, E, F, G, H, I and J respectively. Now we shall write ranks given by the second judge corresponding to the ranks given by the first judge as there are 10 competitors. Now we shall find the total score of 10 C2 pairs of competitors as follows. Now ranks assigned by the first judge to A and B are 1 and 2 respectively since 2 is greater than 1 that is B is greater than A so we assign the score of plus 1 to it. Similarly, ranks assigned by the second judge to A and B are 4 and 6 since 6 is greater than 4 that is B is greater than A so we assign the score of plus 1 to it. So rank of A, B is equal to plus 1 into plus 1 that is plus 1. Ranks given by the first judge to A and C are 1 and 3 respectively since 3 is greater than 1 that is C is greater than A so we assign the score of plus 1 to it. Similarly, ranks given by the second judge to A and C are 4 and 5 respectively since 5 is greater than 4 that is C is greater than A so we assign the score of plus 1 to it. So score of A, C is given by plus 1 into plus 1 that is plus 1. Ranks given by the first judge to A and D are 1 and 4 respectively since 4 is greater than 1 that is D is greater than A so we assign the score of plus 1 to it. Now ranks given by the second judge to A and D are 4 and 7 respectively since 7 is greater than 4 that is D is greater than A so we assign the score of plus 1 to it. So score of A, D will be plus 1 into plus 1 that is plus 1. Now ranks given by the first judge to A and E are 1 and 5 respectively since 5 is greater than 1 that is E is greater than A so we assign the score of plus 1 to it. Now ranks given by the second judge to A and E are 4 and 1 respectively since 1 is less than 4 that is E is less than A so we assign the score of minus 1 to it. So score of A, E will be given by plus 1 into minus 1 that is minus 1 and similarly we shall find the score of A, F, A, G, A, H, A, I and A, J. The score of A, F is minus 1, A, G is minus 1, A, H is plus 1, A, I is plus 1, A, J is plus 1 with a total score of 3. Similarly, score of B, C is given by minus 1, B, D is plus 1, B, E is minus 1, B, F is minus 1, B, G is minus 1, B, H is plus 1, B, I is plus 1, B, J is plus 1 with a total score of 0. Score of C, D is given by plus 1, C, E is minus 1, C, F is minus 1, C, G is minus 1, C, H is plus 1, C, I is plus 1, C, J is plus 1 with a total score of 1. Similarly, score of D, E is minus 1, D, F is minus 1, B, G is minus 1, D, H is plus 1, D, I is plus 1, D, J is plus 1 with a total score of 0. Score of E, F is given by plus 1, E, G is plus 1, E, H is plus 1, E, I is plus 1 and E, J is plus 1 with a total score of 5. Now score of F, G is given by minus 1, F, H is plus 1, F, I is plus 1, F, J is plus 1 with a total score of 2. Now score of G, H is given by plus 1, G, I is given by plus 1, G, J is given by plus 1 with a total score of 3. Now score of H, I is minus 1 and F, J is minus 1 with a total score of minus 2 and score of I, J is minus 1 with a total score of minus 1. Now the net total score is given by 11. From the key idea we know that, Kindle's coefficient of rank correlation denoted by tau is equal to total score by maximum possible score that is 2 F upon N into N minus 1 where N is the number of pairs of observation. So here we have N is equal to 10 as there are 10 competitors and total score is given by 11 that is S is given by 11. Therefore Kindle's coefficient of rank correlation denoted by tau is equal to total score by maximum possible score which is given by 2 N to S upon N into N minus 1 that is 2 N to S S is 11 so we have 2 N to 11 upon N into N minus 1 that is 10 N to 10 minus 1. Which is equal to 2 N to 11 upon 10 into 9 that is 11 upon 45 which is equal to 0.24 therefore Kindle's coefficient of rank correlation is given by 0.24 which is the required answer. This completes our session. Hope you enjoyed this session.