Question

The variance of $20$ observations is $5$. If each observation is multiplied by $2$, then what is the new variance of the resulting observations?

• A. $5$
• B. $10$
• C. $20$
• D. $40$

Answer 1

Answer: (C)

$20$

If each observation is multiplied by $2$, then mean$\left(\mu \right)$ will get doubled.

Now, variance $={\sigma }^2=\frac{(X-\mu {)}^2}{n}$

Now here both $X$ and $\mu$ will be doubled, so the variance will become four times.

Thus, the new variance will be $4$ times the older variance which is $4\times 5=20$.

Hence, C is correct.