Introduction to statistics

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Question

If the S.D. of a set of observations is 8 and if each observation is divided by - 2, the S.D. of the new set of observations will be

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Solution

We know that if X and Y are two variables such that $Y = \frac{X}{a}, a \neq 0$ . Then,
$Y = \frac{X}{a}, a \neq 0$
$∴$ S.D. of the new observations $= \frac{8}{| - 2 |} = 4$

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