Question

Calculate coefficient of correlation of the age of husband and wife using Karl Pearson's method.

Husband (Age)	23	27	28	29	30	31	33	35	36
Wife (Age)	18	20	22	27	29	27	29	28	29

Answer 1

Husband (h)	$h=H-\overline{\mathit{H}}$	h2	Wife (w)	$w=W-\overline{W}$	w2	hw
23 27 28 29 30 31 33 35 36	–7.22 –3.22 –2.22 –1.22 –.22 .78 2.78 4.78 5.78	52.12 10.36 4.92 1.48 0.04 0.60 7.72 22.84 33.40	18 20 22 27 29 27 29 28 29	–7.44 –5.44 –3.44 1.56 3.56 1.56 3.56 2.56 3.56	55.35 29.59 11.83 2.43 12.67 2.43 12.67 6.55 12.67	53.71 17.51 7.63 –1.90 –.78 1.21 9.89 12.23 20.57
∑h = 272		∑h2 = 133.48	∑w = 229		∑w2 = 146.19	∑wh = 120.07

$$\begin{gathered} \mathrm{Mean}\mathrm{age}\mathrm{of}\mathrm{husbands}\left(\overline{H}\right)=\frac{{\sum }_{}^{}h}{n}=\frac{272}{9}=30.22 \\ \mathrm{Mean}\mathrm{age}\mathrm{of}\mathrm{wifes}\left(\overline{W}\right)=\frac{\sum w}{n}=\frac{229}{9}=25.44 \\ r\mathit{=}\frac{\sum wh}{\sqrt{\sum {h^2}_{}\times \sum w^2}}=\frac{120.17}{\sqrt{133.48\times 146.19}}=+0.86 \end{gathered}$$
Thus, there exists a high positive correlation between age of wife and age of husband.