Question

The ages of 5 husbands and their wives are tabulated below. Find the correlation coefficient for their ages.

$\begin{array}{cc}Husban{d}^{\prime }sage\left(X\right)& Wif{e}^{\prime }sage\left(Y\right)\\ 24& 21\\ 28& 28\\ 32& 28\\ 36& 34\\ 40& 39\end{array}$

• A. 0.75
• B. 0.86
• C. 0.97
• D. 0.99

Answer 1

The correct option is C

0.97

$\begin{array}{ccccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (y-\overline{y}{)}^2& (x-\overline{x})(y-\overline{y})\\ 24& 21& -8& 64& -9& 81& 72\\ 28& 28& -4& 16& -2& 4& 8\\ 32& 28& 0& 0& -2& 4& 0\\ 36& 34& 4& 16& 4& 16& 16\\ 40& 39& 8& 64& 9& 81& 72\\ & & & \sum =160& & \sum =186& \sum =168\end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{160}{5}=32$
$\overline{y}=\frac{\sum y}{n}=\frac{150}{5}=30$

$M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}\sqrt{{\sum }_{i=1}^n(y_i-\overline{y}{)}^2}}=\frac{168}{\sqrt{160\times 186}}=\frac{168}{172.5}=0.97$