Central Tendency & DispersionMTP Nov 19Question 3162 of 473
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The Standard Deviation of a set of 50\displaystyle 50 items is 10\displaystyle 10. Find the Standard Deviation if every item is increased by 5\displaystyle 5

Options

A15\displaystyle 15
B5\displaystyle 5
C10\displaystyle 10
DNone of these
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Correct Answer

✅ Option c — 10\displaystyle 10

All Options:

  • A15\displaystyle 15
  • B5\displaystyle 5
  • C10\displaystyle 10
  • DNone of these

Detailed Solution & Explanation

**Given:** SD = 10, n=50\displaystyle n = 50. Every item is increased by 5. **Concept:** Adding a constant to every observation does NOT change the Standard Deviation. This is because SD measures spread around the mean, and when all values shift by the same amount, the relative spread remains unchanged. **Proof:** If xi′=xi+5\displaystyle x_i' = x_i + 5, then xˉ′=xˉ+5\displaystyle \bar{x}' = \bar{x} + 5. xi′−xˉ′=(xi+5)−(xˉ+5)=xi−xˉx_i' - \bar{x}' = (x_i + 5) - (\bar{x} + 5) = x_i - \bar{x} Deviations unchanged ⇒\displaystyle \Rightarrow SD unchanged. **New SD = Old SD = 10** (Option C). The given `correct_option` 'b' (5) is incorrect. Hence, **Option C** is the correct answer.

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