Question

The marks of some students were listed out of 75. The SD 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. None of these

Answer 1

Answer: (A)

Given, $\sigma =9$
Let a student obtains x out of 75. Then his marks out of 100 are $\frac{4x}{3}.$ Each observation is multiplied by $\frac{4}{3}$
Now $\sigma =\frac{4}{3}\times 9=12$, Variance $={\sigma }^2=144$