 Hello and welcome to the session. In this session we are going to discuss the following question which says that calculate Cal Pearson's coefficient of correlation for the following series where x series is given by 52, 58, 55, 50, 47, 35, 63, 45, 44 and 70 and the y series is given by 48, 62, 52, 49, 55, 56, 64, 49, 52 and 68. When the deviation is taken from an assumed mean then Cal Pearson's coefficient of correlation denoted by rho of x, y is given by summation u v minus summation of u into summation of v by n whole upon square root of summation u square minus summation u v whole square by n into square root of summation v square minus summation v v whole square by n where u is equal to x minus a or x minus a by h and v is equal to y minus b or y minus b by h where a and b are the assumed means and n is the number of pairs of observation this formula is used when actual means are fractions with this key idea we shall proceed with the solution. We are given the following data here summation of x that is sum of all the values of x is given by 519 and summation of y that is sum of all the values in y is given by 555 also n that is the number of pairs of observation is 10 and we know that a and b are the assumed means a is given by summation of x by n that is 519 by 10 which is equal to 51.9 and b is given by summation of y by n that is 555 by 10 which is equal to 65.5 since a and b are in fractions therefore we take assumed mean for x series as 52 and for y series as 55 and we know that u is given by x minus a and v is given by y minus b u is equal to x minus a and a is equal to 52 so we have 52 minus 52 that is 0 58 minus 52 is 6, 55 minus 52 is 3, 59 is 52 is minus 2, 47 minus 52 is minus 5, 35 minus 52 is minus 17, 63 minus 52 is 11, 45 minus 52 is minus 7, 44 minus 52 is minus 8, 79 is 52 is 18 and v is given by y minus b and v is equal to 55 so we have 48 minus 55 that is minus 7, 62 minus 55 is 7, 52 minus 55 is minus 3, 49 minus 55 is minus 6, 55 minus 55 is 0, 56 minus 55 is 1, 64 minus 55 is 9, 49 minus 55 is minus 6, 52 minus 55 is minus 3, 68 minus 55 is 13. Now we shall find out u square, v square and u v, u square is given by 0 square that is 0, 6 square is 36, 3 square is 9, minus 2 square is 4, minus 5 square is 25, minus 17 square is 289, 11 square is 121, minus 7 square is 49, minus 8 square is 64, 18 square is 324, v square is given by minus 7 square that is 49, 7 square is 49, minus 3 square is 9, minus 6 square is 36, 0 square is 0, 1 square is 1, 9 square is 81, minus 6 square is 36, minus 3 square is 9, 13 square is 169. u into v is given by 0 into minus 7 that is 0, 6 into 7 that is 42, 3 into minus 3 is minus 9, minus 2 into minus 6 is 12, minus 5 into 0 is 0, minus 17 into 1 is minus 17, 11 into 9 is 99, minus 7 into minus 6 is 42, minus 8 into minus 3 is 24, 18 into 13 is 234, now summation of u that is some of all the values in u is given by minus 1 and summation of v that is some of all the values in v is given by 5. summation u square that is sum of all the values in u square is given by 921,heiro Summation v square, that is, sum of all the values in v square is given by 439. Summation u v, that is, sum of all the values in u into v, that is, 427. Now, we know that when deviation is taken from an assumed mean, then calculation coefficient of correlation denoted by rho of x, y is given by summation u v minus summation u into summation v by n whole upon square root of summation u square minus summation u v whole square by n into square root of summation v square minus summation v v whole square by n. So, we have calculation coefficient of correlation rho of x, y is equal to summation u v, that is, 427 minus summation u into summation v, that is minus 1 into size by n, that is, 10 whole upon square root of summation u square, that is, 921 minus summation u v whole square by n, that is, minus 1 square by 10 into square root of summation v square, that is, 439 minus summation v v whole square by n, that is, 5 square by 10, which is equal to 427 plus 0.5 whole upon square root of 921 minus 0.1 into square root of 439 minus 2.5, which is equal to 427.5 upon square root of 920.9 into 436.5, which is equal to 427.5 upon square root of 401,972.85, which is equal to 427.5 upon 634.01, which is equal to 0.674. Hence, called Pearson's coefficient of correlation is given by 0.674, which is the required answer. This completes our session, hope you enjoyed this session. Hence, called Pearson's coefficient of correlation is given by 0.673, which is the required answer. This completes our session, hope you enjoyed this session.