Measures of Central Tendency and DispersionMCQMTP 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.

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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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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