Question

The marks of some students were listed out of 75. The standard deviation of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is :

• A. 144
• B. 122
• C. 81
• D. 3

Answer 1

The correct option is A 144

Given$,$ $\sigma =9$

Let a student obtains $X$ marks out of $75.$ Then$,$ his marks out of $100$ are $\frac{100}{75}X=\frac{4}{3}X$

Each observation is multiply by $\frac{4}{3}$

$\therefore$ New $SD,$ ${\sigma }_{new}=\frac{4}{3}\times 9=12$

So$,$ variance is ${\sigma }_{new}^2=144$

Hence,

option $\left(A\right)$ is correct answer.