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

1. A

81

2. B

122

3. C

144

4. D

None of these

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### Solution:

Given, $\mathrm{\sigma }$ =9
Let a student obtains x marks out of  75. Then, his marks out of

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

Now, $\mathrm{SD},\mathrm{\sigma }=\frac{4}{3}×9=12$

Hence, variance is ${\mathrm{\sigma }}^{2}=144$

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