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

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

Solution:

Given, $σ$ =9
Let a student obtains x marks out of 75. Then, his marks out of

100 are $\frac{4 x}{3}$ .Each observation multiple by $\frac{4}{3}$

Now, $SD, σ = \frac{4}{3} \times 9 = 12$

Hence, variance is $σ^{2} = 144$

Related content

Appreciation Words

Wave Optics Mind Map

Alternating Current Mind Map for Class 12, JEE & NEET

Paramedical Courses After Class 10

Top Courses After 12th Science with PCM, PCB and PCMB

Subject Change Application in School and College

CBSE Class 10 Result 2024: Is the Release Date Early? Check Expected Schedule

Mizoram NEET Merit List 2023

Government Jobs After 12th Arts Stream

Chhattisgarh NEET UG Merit List 2023