Question

The variance of $5$ numbers is $10$. If each number is divided by $2$, then the variance of new numbers is

• A. $5.5$
• B. $2.5$
• C. $5$
• D. None of these

Answer 1

The correct option is B $2.5$

Given that variance of $5$ number is $10$

Therefore, $Var\left(X\right)=10$

Given that each number is divided by $2$

Therefore, variance of new numbers is $Var\left(\frac{X}{2}\right)$

$Var\left(\frac{X}{2}\right)=\frac{1}{4}Var\left(X\right)=\frac{1}{4}\left(10\right)=2.5$

Hence, variance of new numbers is $2.5$