Central Tendency & DispersionMTP May 19 Series IIQuestion 3154 of 473

If all the observations are multiplied by 2, then

ANew SD would be also multiplied by 2

BNew SD would be half of the previous SD

CNew SD would be increased by 2

DNew SD would be decreased by 2

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Correct Answer

✅ Option a — New SD would be also multiplied by 2

**Concept:** When every observation is multiplied by a constant

\displaystyle k

, the Standard Deviation is also multiplied by

\displaystyle |k|

. **Proof:** If

\displaystyle x_i' = 2x_i

, then

\displaystyle \bar{x}' = 2\bar{x}

\sigma' = \sqrt{\frac{\sum(x_i' - \bar{x}')^2}{n}} = \sqrt{\frac{\sum(2x_i - 2\bar{x})^2}{n}} = \sqrt{\frac{4\sum(x_i - \bar{x})^2}{n}} = 2\sigma

So the new SD = 2 × old SD (multiplied by 2). Hence, **Option A** is the correct answer.

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