Question

The marks of some students were listed from total marks 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. $81$
• B. $122$
• C. $144$
• D. $196$

Answer 1

The correct option is C $144$

Given : $\sigma =9$
Let a student obtains $X$ marks out of $75$.
Then his/her marks out of $100$ is
$\frac{100}{75}X=\frac{4}{3}X$

So, each observation should be multiplied by $\frac{4}{3}$ for obtaining new data set.
Hence, new variance $={\left(\frac{4}{3}\right)}^2\times 9^2=144$