Question

The coefficient of correlation between two variables x and y is 0.5, their covariance is 16. If the S.D of x is 4, then the S.D. of y is equal to

• A. 4
• B. 8
• C. 16
• D. 64

Answer 1

Answer: (B)

8

Answer 2

We have, $r_{xy} = 0.5,$ $Cov(x,y) = 16$. S.D of x i.e., $\sigma_{x} = 4$, $\sigma_{y} = ?$

We know that, $r(x,y) = \frac{Cov(x,y)}{\sigma_{x}.\sigma_{y}}$

$0.5 = \frac{16}{4.\sigma_{y}}$; ∴ $\sigma_{y} = 8$.