Question

If the difference between the standard deviation and
variance of a data is 12 then find the sum of the variance and standard deviation of that data

• A. 20
• B. 15
• C. 18
• D. 22

Answer 1

The correct option is A 20

We know that if S.D. $=\sigma$, then Variance $={\sigma }^2$
Given, ${\sigma }^2-\sigma =12$
$\Rightarrow {\sigma }^2-4\sigma +3\sigma -12=0$
$\Rightarrow \sigma (\sigma -4)+3(\sigma -4)=0$
$\Rightarrow (\sigma +3)(\sigma -4)=0$
$\Rightarrow \sigma =-3,4$
As S.D. is square root of variance, it is a positive value.
So, S.D $=4$
And S.D $+$ Variance $=4+4^2=4+16=20$