calculate the correlation coefficient (to three decimal places)

Question

Based on the data shown below, calculate the correlation coefficient (to three decimal places)

xy
3	79.2
4	82.2
5	78.4
6	80.4
7	79.2
8	88
9	88.4
10	88.2
11	88.2

r=

Answer 1

n=9

∑x_i = 63

Mean_x = M_x = 63/9 = 7

∑(x_i - M_x)² = SS_x = 60

∑y_i = 752.6

Mean_y = M_y = 752.6/9 = 83.622

∑(y_i - M_y)² = SS_y = 166.516

∑(x_i - M_x)(y_i - M_y) = 82.8

r = ∑((x_i - M_y)(y_i - M_x)) / √((SS_x)(SS_y))

r = 82.8 / √((60)(166.516)) ≈ 0.828