Question

Find out coefficient of correlation between the age of Husband and Wife, using Karl Pearson's method based on actual mean value of the following series.

Age of Husband	20	23	27	31	35	38	40	42
Age of Wife	18	20	24	30	32	34	36	38

Answer 1

Age of husband (X)	Deviation $\mathit{x}\mathit{=}\mathit{X}\mathit{-}\overline{\mathit{X}}$	Square of deviation x2	Age of wife (Y)	Deviation $\mathit{y}\mathit{=}\mathit{Y}\mathit{-}\overline{\mathit{Y}}$	Square of deviation y2	xy
20 23 27 31 35 38 40 42	−12 −9 −5 −1 3 6 8 10	144 81 25 1 9 36 64 100	18 20 24 30 32 34 36 38	−11 −9 −5 1 3 5 7 9	121 81 25 1 9 25 49 81	132 81 25 −1 9 30 56 90
ΣX = 256		$\sum _{}^{}{x}^2=460$	$\sum _{}^{}Y=232$		$\sum _{}{y}^2=392$	${\sum }_{}^{}xy=422$

$$\begin{gathered} \overline{\mathrm{X}}=\frac{\mathrm{\Sigma X}}{\mathrm{N}}=\frac{256}{8}=32 \\ \overline{\mathrm{Y}}=\frac{\mathrm{\Sigma Y}}{\mathrm{N}}=\frac{232}{8}=29 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2\times \mathrm{\Sigma }{y}^2}} \\ \mathrm{or},r=\frac{422}{\sqrt{460\times 392}} \\ \mathrm{or},r=\frac{422}{\sqrt{180320}} \\ \mathrm{or},r=\frac{422}{424.64}= \\ \Rightarrow r=+0.994 \end{gathered}$$

Thus, the coefficient of correlation between husband's age and wife's age is +0.994.