Measures of Central Tendency and DispersionMCQPYQ Dec 22Question 3223 of 473
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If the first quartile in 56.50\displaystyle 56.50 and the third quartile is 77.50\displaystyle 77.50, then the co-efficient of QD is:

Options

A18.09\displaystyle 18.09
B15.67\displaystyle 15.67
C63.80\displaystyle 63.80
D156.71\displaystyle 156.71
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Correct Answer

✅ Option b — 15.67\displaystyle 15.67

All Options:

  • A18.09\displaystyle 18.09
  • B15.67\displaystyle 15.67
  • C63.80\displaystyle 63.80
  • D156.71\displaystyle 156.71

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Detailed Solution & Explanation

We are given: - First quartile: Q1=56.50\displaystyle Q_1 = 56.50 - Third quartile: Q3=77.50\displaystyle Q_3 = 77.50 The coefficient of quartile deviation is calculated as: Coefficient of Q.D.=Q3−Q1Q3+Q1×100\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100 Coefficient of Q.D.=77.50−56.5077.50+56.50×100=21134×100≈15.67%\text{Coefficient of Q.D.} = \frac{77.50 - 56.50}{77.50 + 56.50} \times 100 = \frac{21}{134} \times 100 \approx 15.67\% Hence, **Option B** 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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