Question

If the variance of a list containing number $7,9,15,16,18$ is $18$ then the variance of list containing numbers $12,16,28,30,34$ will be

• A. $18$
• B. $36$
• C. $72$
• D. $76$

Answer 1

The correct option is C $72$

$\left\{X_i\right\}=\{7,9,15,16,18\}$

As we can observe
observation $X_i^{\prime }=2\times \left\{X_i\right\}-2$
Using property variance: Variance depends on only scale ($x\to {\sigma }^2\Rightarrow kx\to k^2{\sigma }^2$)
$\therefore \text{Variance}{\sigma }^{\prime 2}=2^2\times \text{Variance}\left({\sigma }^2\right){\sigma }^{\prime 2}=4\times 18=72$