Question

Compute coefficient of correlation from the following data:

Sum of products of deviations of X and Y series from their respective mean is 20. Number of pairs of observations is 10.

Answer 1

Given : $\sum (X-\overline{X}{)}^2=144,,\sum (Y-\overline{Y}{)}^2=225,\sum (X-\overline{X})(Y-\overline{Y})=20,N=10r=\frac{\sum (X-\overline{X})(Y-\overline{Y})}{\sqrt{\sum (X-\overline{X}{)}^2}\sqrt{\sum (Y-\overline{Y}{)}^2}}=\frac{20}{\sqrt{144}\sqrt{225}}=\frac{20}{12\times 15}=+0.11$