Question

The coefficient of correlation if $\overline{x}=\overline{y}=0$, ${\sum }^{}{x}_i{y}_i=12,{\sigma }_x=4,{\sigma }_y=4$ and $n=10$ is

• A. $0.4$
• B. $0.3$
• C. $0.2$
• D. $0.1$

Answer 1

Answer: (D)

$0.1$

$r_{xy}=\frac{Cov(x,y)}{{\sigma }_x{\sigma }_y}=\frac{\frac{1}{n}\left[{\sum }_{i=1}^n{x}_i{y}_i-\overline{x}\overline{y}\right]}{{\sigma }_x{\sigma }_y}$
$\therefore r_{xy}=\frac{\sum x_i{y}_i}{{\sigma }_x{\sigma }_y.n}(\because \overline{x}=\overline{y}=0)$
using ${\sigma }_x=3,{\sigma }_y=4,n=10$ we have
$r_{xy}=\frac{12}{3\times 4\times 10}=0.1$