Question

From the following data compute the product moment correlation between X and Y.

	X series	Y series
Arithmetic Mean	25	18
Sum of Square of deviations from Arithmetic Mean	136	138

Summation of products of deviations of X and Y series from their respective means = 122
Number of points of values = 15

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \begin{array}{ccc}\overline{X}=25& \mathrm{\Sigma }{x}^2=136& \mathrm{\Sigma }xy=122\\ \overline{Y}=18& \mathrm{\Sigma }{y}^2=138& n=15\end{array} \\ \mathrm{Now}, \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ r=\frac{122}{\sqrt{136}\times \sqrt{138}}=\frac{122}{\sqrt{136\times 138}}=\frac{122}{11.66\times 11.74} \\ r=\frac{122}{136.996}=0.89 \end{gathered}$$
Thus, the product moment correlation between X and Y is 0.89.