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

Answer: (A)

$20$

Given that difference between the standard deviation($\sigma$) and variance(${\sigma }^2$) is $12$.

$⟹{\sigma }^2-\sigma =12$

$⟹{\sigma }^2-\sigma -12=0$

$⟹{\sigma }^2-4\sigma +3\sigma -12=0$

$⟹\sigma (\sigma -4)+3(\sigma -4)=0$

$⟹(\sigma +3)(\sigma -4)=0$

$⟹\sigma =-3$ (or) $\sigma =4$

Since, standard deviation is always $\ge 0$

Therefore, $\sigma =4$

$⟹{\sigma }^2=4^2=16$

${\sigma }^2+\sigma =16+4=20$

Therefore sum of the standard deviation($\sigma$) and variance(${\sigma }^2$) is $\sigma +{\sigma }^2=20$