 Hello and welcome to the session. In this session we are going to discuss the following question which says that, Calculate Khan Pearson's Co-efficient of Co-relation for the following data where x series is given as 44, 45, 47, 49, 51, 53, 55, 57, 59, 60 and y series is given as 36, 30, 39, 43, 41, 45, 46, 49, 51, 50. We know that, Khan Pearson's Co-efficient of Co-relation denoted by rho of x, y or r is given by summation dx into dy upon square root of summation dx square into summation dy square where dx and dy are the deviations from the actual mean dx is given by x minus x bar where x bar is equal to summation of x by n and dy is given by y minus y bar where y bar is equal to summation of y by n and n is the number of individuals in each series. With this key idea we shall proceed with the solution. We are given the following data here summation of x that is the sum of all the elements in x is given by 520 and summation of y that is sum of all the elements in y is given by 440 also n that is the number of individuals in each series is 10 and we know that x bar is given by summation of x by n so we have x bar is equal to summation of x that is 520 and n that is 10 which is equal to 52 and y bar is given by summation of y by n that is y bar is equal to summation y that is 430 by 10 which is equal to 44 and some of the key idea we know that dx is given by x minus x bar and dy is given by y minus y bar dx is given by x minus x bar and x bar is equal to 52 so we have 34 minus 52 that is minus 8, 45 minus 52 is minus 7, 47 minus 52 is minus 5, 49 minus 52 is minus 3, 51 minus 52 is minus 1, 53 minus 52 is 1, 55 minus 52 is 3, 57 minus 52 is 5, 59 minus 52 is 7, 60 minus 52 is 8 and dy is given by y minus y bar where y bar is equal to 34 that is 36 minus 34 is minus 8, 30 minus 34 is minus 4, 39 minus 34 is minus 5, 33 minus 34 is minus 1, 41 minus 34 is minus 3, 35 minus 34 is 1, 36 minus 34 is 2, 39 minus 34 is 5, 51 minus 34 is 7, 50 minus 34 is 6. Next we shall find out dx square dy square and dx dy. dx square is given by minus 8 square that is 64 minus 7 square is 49 minus 5 square is 25 minus 3 square is 9 minus 1 square is 1, 1 square is 1, 3 square is 9, 5 square is 25, 7 square is 49, 8 square is 64. dy square is given by minus 8 square that is 64 minus 4 square is 16 minus 5 square is 25 minus 1 square is 1 minus 3 square is 9, 1 square is 1, 2 square is 4, 5 square is 25, 7 square is 49, 6 square is 36. And dx dy is given by minus 8 into minus 8 that is 64 minus 7 into minus 4 is 28, minus 5 into minus 5 is 25, minus 3 into minus 1 is 3, minus 1 into minus 3 is 3, 1 into 1 is 1, 3 into 2 is 6, 5 into 5 is 25, 7 into 7 is 49 and 8 into 6 is 38. Also we have summation dx square that is sum of all the elements in dx square is given by 296, summation dy square that is sum of all the elements in dy square is given by 230, summation dx into dy that is sum of all the elements in dx dy is given by 252. And from the key idea we know that Carl Pearson's coefficient of correlation denoted by rho of xy or r is given by summation dx into dy whole upon square root of summation dx square into summation dy. So we have rho of xy or r given by summation dx into dy that is 252 upon square root of summation dx square that is 296 into summation dy square that is 230. Which is equal to 252 upon square root of 680 which is equal to 252 upon 260.921 which is equal to 0.9658 which is equal to 0.9658. Hence Carl Pearson's coefficient of correlation is given by 0.9658 which is the required answer. This completes our session. Hope you enjoyed this session.