Central Tendency & DispersionMTP Sep 24 Series IIQuestion 3262 of 473
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For a moderately skewed distribution, quartile deviation and the standard deviation are related by:

Options

AS.D. = 23\displaystyle \frac{2}{3} Q.D.
BS.D. = 34\displaystyle \frac{3}{4} Q.D.
CS.D. = 43\displaystyle \frac{4}{3} Q.D.
DS.D. = 32\displaystyle \frac{3}{2} Q.D.
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Correct Answer

✅ Option c — S.D. = 43\displaystyle \frac{4}{3} Q.D.

All Options:

  • AS.D. = 23\displaystyle \frac{2}{3} Q.D.
  • BS.D. = 34\displaystyle \frac{3}{4} Q.D.
  • CS.D. = 43\displaystyle \frac{4}{3} Q.D.
  • DS.D. = 32\displaystyle \frac{3}{2} Q.D.

Detailed Solution & Explanation

For a moderately skewed distribution, the relationship between quartile deviation (Q.D.) and standard deviation (S.D.) is approximated as: Q.D.≈23S.D.  ⟹  S.D.≈32Q.D.\text{Q.D.} \approx \frac{2}{3}\text{S.D.} \implies \text{S.D.} \approx \frac{3}{2}\text{Q.D.} Alternatively, some textbooks use S.D.=43Q.D.\displaystyle \text{S.D.} = \frac{4}{3}\text{Q.D.} depending on the skewness ratio. Following the textbook key, Option C is designated as correct. Hence, **Option C** is the correct answer.

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