 Hello and welcome to the session. In this session we are going to discuss the following question which says that find the coefficient of correlation from the following pair of observations. Also comment on the nature of r. Let's start with the solution. We are given the distribution as follows. Now we shall find xi square, yi square and xi into yi. Now xi square is given by 2 square that is 4, 4 square 16, 6 square 36, 8 square 64, 10 square 100 and 12 square 144. Y square is given by 3 square 9, 5 square 25, 7 square 49, 9 square 81, 11 square 121, 13 square 169 and xi yi is given by 2 into 3 that is 6, 4 into 5, 20, 6 into 7, 42, 8 into 9, 72, 10 into 11, 110, 12 into 13, 156. Now summation of xi that is sum of all the elements of xi is given by 32. Summation of yi that is sum of all the elements of yi is given by 38. Summation of xi square is given by 364. Summation of yi square is given by 454 and summation of xi yi is given by 406. Here the value of n that is the number of elements is given by 6. Now we know that coefficient of correlation r is given by summation of xi into yi minus summation xi into summation yi by n whole upon square root of summation xi square minus summation xi square by n into summation yi square minus summation yi square by n which is equal to summation xi yi is equal to 406 minus summation xi is 42 into summation yi which is 48 by 6 whole upon square root of summation xi square that is 364 minus summation xi the whole square that is 42 square by 6 into summation yi square that is 454 minus summation yi the whole square that is 48 square by 6 which is equal to 406 minus 336 upon square root of 364 minus 294 into 454 minus 384 which is equal to 70 upon square root of 70 into 70 that is equal to 70 by 70 which is equal to 1. Therefore coefficient of correlation is given by 1 since r is equal to 1. So there is a functional linear relationship between these variables xi and yi that is there exist constant a and b where b is greater than or equal to 0 such that yi is equal to a plus b xi now we shall draw the scatter diagram to draw the scatter diagram we take xi on the horizontal axis and yi on the vertical axis now we shall plot the points on the graph and the points are 23456789 1011 and 1213 now the points are 23456789 1011 and 1213 now this is the required scatter diagram the points in the scatter diagram proceed in a line from bottom to the top which indicates that xi and yi are in perfect positive correlation therefore there is a perfect positive correlation between xi and yi this completes our session hope you enjoyed this session