Question

If each observation is of raw data whose variance is ${\sigma }^2$ is multiplied by $h$, then the variance of the new set is

• A. ${\sigma }^2$
• B. $h^2{\sigma }^2$
• C. $h{\sigma }^2$
• D. $h+{\sigma }^2$

Answer 1

Answer: (B)

$h^2{\sigma }^2$

We know $Var(ax+b)=a^2.Var\left(x\right)$
Here $a=h,b=0$
$\therefore Var(h.x)=h^2.Var\left(x\right)=h^2{\sigma }^2$