Central Tendency & DispersionMTP May 18Question 3158 of 473
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The SD is independent of change of

Options

AOrigin
BScale
CBoth (a) & (b)
DNone of these
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Correct Answer

✅ Option a — Origin

All Options:

  • AOrigin
  • BScale
  • CBoth (a) & (b)
  • DNone of these

Detailed Solution & Explanation

**Properties of Standard Deviation:** 1. **Change of Origin (adding/subtracting a constant):** SD is INDEPENDENT of change of origin. If xi′=xi+c\displaystyle x_i' = x_i + c, then σx′=σx\displaystyle \sigma_{x'} = \sigma_x. 2. **Change of Scale (multiplying/dividing by a constant):** SD is NOT independent of change of scale. If xi′=kxi\displaystyle x_i' = kx_i, then σx′=∣k∣σx\displaystyle \sigma_{x'} = |k|\sigma_x. **Therefore:** SD is independent only of change of **origin**, not of scale. The given `correct_option` is 'b' (Scale), which is WRONG because SD is actually AFFECTED by change of scale. SD is independent of change of **origin** (Option A). Hence, **Option A** is the correct answer.

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