Question

Calculate coefficient of correlation for the ages of husband and wife.

Age of husband	24	25	22	30	34	37
Age of wife	20	21	18	26	28	30

Answer 1

Age of Husband (X)	Age of Wife (Y)	X2	Y2	XY
24 25 22 30 34 37	20 21 18 26 28 30	576 625 484 900 1156 1369	400 441 324 676 784 900	480 525 396 780 952 1110
$\mathit{\Sigma }\mathit{X}$=172	$\mathit{\Sigma }\mathit{Y}$=143	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=5110	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=3525	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=4243

N = 6

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma \mathrm{X\Sigma }Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma {\mathrm{Y}}^2-{\left(\Sigma Y\right)}^2}} \\ or,r=\frac{6\times 4243-172\times 143}{\sqrt{6\times 5110-{\left(172\right)}^2}\sqrt{6\times 3525-{\left(143\right)}^2}} \\ or,r=\frac{862}{32.80\times 26.47} \\ \Rightarrow r=0.992 \end{gathered}$$

Thus, the coefficient of correlation for the ages of husband and wife is 0.992.