Question

Number of pairs of observations of X and Y series = 10 .
X series : Arithmetic Average = 65
: Standard Deviation = 23.33
Y series : Arithmetic Average = 66
Standard deviation = 14.9
Summation of products of corresponding deviations of X and Y series from their respective means = 2704.
Calculate product moment correlation of X and Y series.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \overline{X}=65 \\ \overline{Y}=66 \\ {\sigma }_x=23.33 \\ \sigma y=14.9 \end{gathered}$$

Now,
$$\begin{gathered} r=\frac{\mathrm{\Sigma }xy}{N·{\mathrm{\sigma }}_x{\mathrm{\sigma }}_y} \\ =\frac{2704}{10\times 23.33\times 14.9} \\ =\frac{2704}{3476.17} \\ =0.7778\mathrm{or}0.78(\mathrm{approx}.) \end{gathered}$$
Thus, product moment correlation of X and Y series is 0.78.