Question

Calculate the coefficient of correlation for the following ages of husbands and wives in years at the time of their marriage.

Age of Husbands	:	23	27	28	28	29	30	31	33	35	36
Age of Wives	:	18	20	22	27	21	29	27	29	28	29

Answer 1

Husband (X)	Wife (Y)	$\left(\mathit{X}\mathit{-}\overline{X}\right)$ x	x2	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ y	y2	xy
23	18	−7	49	−7	49	49
27	20	−3	9	−5	25	15
28	22	−2	4	−3	9	6
28	27	−2	4	2	4	−4
29	21	−1	1	−4	16	4
30	29	0	0	4	16	0
31	27	1	1	2	4	2
33	29	3	9	4	16	12
35	28	5	25	3	9	15
36	29	6	36	4	16	24
ƩX = 300	ƩY = 250		Ʃx2 =138		Ʃy2 =164	Ʃxy =123

N = 10

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{300}{10}=30 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{250}{10}=25 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ =\frac{123}{\sqrt{138}\times \sqrt{164}} \\ =\frac{123}{11.74\times 12.80} \\ =0.818\mathrm{or}0.82(\mathrm{approx}.) \end{gathered}$$

Thus, there exists high positive correlation between age of husband and age of wife.