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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 calculate. Then twice the new variance is:

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Detailed 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 is multiply by $\frac{4}{3} .$

$∴$ New $S D, σ = \frac{4}{3} \times 9 = 12 \Rightarrow σ^{2} = 144$

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