Variance of 10 observations is 16 . If each observation is doubled, then standard deviation&nbs

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The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -

A

$16$

B

$32$

C

$8$

D

$4$

Solution

$\operatorname{Var}\left(a x_{i}+b\right)=a^{2} \operatorname{var}\left(x_{i}\right)$

Variance on doubling each observation

$=2^{2} \times 16=64$

Std. deviation $=\sqrt{\operatorname{var}}=8$

Standard 11

Mathematics

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