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  4. 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

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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

Statistics

Solution:

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 $\sigma=\frac{4}{3}\times9=12$, Variance $=\sigma^{2}=144$