If the SD of a variable X is sigma then Quartile Deviation (QD) is

Option c: 2/3 sigma. Solution: For a normal distribution, the Quartile Deviation (Q.D.) is related to the standard deviation ( sigma ) by the approximation: Q.D. ≈ 0.675 sigma ≈ 2/3 sigma Hence, Option C is the correct answer.

If the SD of a variable $X$ is $\sigma$ then Quartile Deviation (QD) is

The correct answer is Option c: $\frac{2}{3} \sigma$. For a normal distribution, the Quartile Deviation (Q.D.) is related to the standard deviation ($\sigma$) by the approximation: $$\text{Q.D.} \approx 0.675 \sigma \approx \frac{2}{3} \sigma$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 18Question 3249 of 473

All Questions

If the SD of a variable $\displaystyle X$ is $\displaystyle \sigma$ then Quartile Deviation (QD) is

Options

\displaystyle \frac{4}{5} \sigma

\displaystyle \frac{3}{2} \sigma

\displaystyle \frac{2}{3} \sigma

\displaystyle \frac{5}{4} \sigma

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Correct Answer

✅ Option c — $\displaystyle \frac{2}{3} \sigma$

All Options:

A $\displaystyle \frac{4}{5} \sigma$
B $\displaystyle \frac{3}{2} \sigma$
C $\displaystyle \frac{2}{3} \sigma$
D $\displaystyle \frac{5}{4} \sigma$

Detailed Solution & Explanation

For a normal distribution, the Quartile Deviation (Q.D.) is related to the standard deviation (

\displaystyle \sigma

) by the approximation:

\text{Q.D.} \approx 0.675 \sigma \approx \frac{2}{3} \sigma

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.

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If the SD of a variable X\displaystyle XX is σ\displaystyle \sigmaσ then Quartile Deviation (QD) is