Question

If $n=10,\sum x=4,\sum y=3,\sum x^2=8,\sum y^2=9$ and $\sum xy=3,$ then the coefficient of $r_{x,y}$ is

• A. $\frac{3}{4}$
• B. $\frac{1}{5}$
• C. $\frac{1}{6}$
• D. $\frac{1}{4}$

Answer 1

Answer: (D)

$\frac{1}{4}$

Correlation coefficient
$r_{x,y}=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^2-{(\sum x)}^2][n\sum y^2-{(\sum y)}^2]}}$
$=\frac{30-12}{\sqrt{64\times 81}}$
$\Rightarrow r_{x,y}=\frac{1}{4}$