Measures of Central Tendency and DispersionMCQPYQ June 19Question 3218 of 473
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Coefficient of quartile deviation is 1/4\displaystyle 1/4 then Q3/Q1\displaystyle Q_3 / Q_1

Options

A53\displaystyle \frac{5}{3}
B43\displaystyle \frac{4}{3}
C34\displaystyle \frac{3}{4}
D35\displaystyle \frac{3}{5}
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Correct Answer

✅ Option a — 53\displaystyle \frac{5}{3}

All Options:

  • A53\displaystyle \frac{5}{3}
  • B43\displaystyle \frac{4}{3}
  • C34\displaystyle \frac{3}{4}
  • D35\displaystyle \frac{3}{5}

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Detailed Solution & Explanation

We are given the coefficient of quartile deviation is 14\displaystyle \frac{1}{4}: Coefficient of Q.D.=Q3−Q1Q3+Q1=14\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} = \frac{1}{4} Cross-multiply to solve for the ratio Q3Q1\displaystyle \frac{Q_3}{Q_1}: 4(Q3−Q1)=Q3+Q14(Q_3 - Q_1) = Q_3 + Q_1 4Q3−4Q1=Q3+Q14Q_3 - 4Q_1 = Q_3 + Q_1 3Q3=5Q1  ⟹  Q3Q1=533Q_3 = 5Q_1 \implies \frac{Q_3}{Q_1} = \frac{5}{3} Hence, **Option A** 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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