Central Tendency & DispersionMTP Sep 24 Series IQuestion 3214 of 473
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If the same amount is added or subtracted from all the of an individual series then the standard deviation and variance both shall be

Options

AChanged
BUnchanged
CSame
DNone of these
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Correct Answer

✅ Option b — Unchanged

All Options:

  • AChanged
  • BUnchanged
  • CSame
  • DNone of these

Detailed Solution & Explanation

**Concept:** Adding or subtracting a constant from all observations changes the **origin** of the data but does NOT change the spread. **Proof:** If xi′=xi±c\displaystyle x_i' = x_i \pm c, then xˉ′=xˉ±c\displaystyle \bar{x}' = \bar{x} \pm c. - Deviation: xi′−xˉ′=(xi±c)−(xˉ±c)=xi−xˉ\displaystyle x_i' - \bar{x}' = (x_i \pm c) - (\bar{x} \pm c) = x_i - \bar{x} (unchanged) - Variance: σ′2=∑(xi−xˉ)2n=σ2\displaystyle \sigma'^2 = \frac{\sum(x_i - \bar{x})^2}{n} = \sigma^2 (unchanged) - SD: σ′=σ\displaystyle \sigma' = \sigma (unchanged) **Both SD and Variance remain Unchanged.** Hence, **Option B** is the correct answer.

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