Q. 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) 81
B) 122
C) 144
D) None of these
Explanation
(c)
Given, $\sigma = 9$
Let a student obtains $x$ marks out of 75. Then, his marks out of 100 are$\frac{4x}{3}$. Each observation is multiply by $\frac{4}{3}$
$\therefore New\ SD,\ \sigma = \frac{4}{3} \times 9 = 12$
Hence, variance is $\sigma^{2} = 144$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.