Measures of Central Tendency and DispersionPYQ Jan 26Question 4287 of 473
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Calculate the coefficient of quartile deviation for 11, 55, 65, 22, 33, 98, 88

Options

A6
B166.6
C60
D0.6
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Correct Answer

✅ Option c — 60

All Options:

  • A6
  • B166.6
  • C60
  • D0.6

Detailed Solution & Explanation

First, let us arrange the given data in ascending order: 11,22,33,55,65,88,9811, 22, 33, 55, 65, 88, 98 The number of observations is N=7\displaystyle N = 7.
We calculate the first quartile (Q1\displaystyle Q_1) and the third quartile (Q3\displaystyle Q_3): - **First Quartile (Q1\displaystyle Q_1)**: Q1=Value of (N+14)-th termQ_1 = \text{Value of } \left( \frac{N+1}{4} \right)\text{-th term} Q1=Value of (7+14)-th term=Value of 2-nd termQ_1 = \text{Value of } \left( \frac{7+1}{4} \right)\text{-th term} = \text{Value of } 2\text{-nd term} Q1=22Q_1 = 22
- **Third Quartile (Q3\displaystyle Q_3)**: Q3=Value of 3×(N+14)-th termQ_3 = \text{Value of } 3 \times \left( \frac{N+1}{4} \right)\text{-th term} Q3=Value of 3×2=Value of 6-th termQ_3 = \text{Value of } 3 \times 2 = \text{Value of } 6\text{-th term} Q3=88Q_3 = 88
Now we calculate the coefficient of quartile deviation: Coefficient of Quartile Deviation=Q3−Q1Q3+Q1\text{Coefficient of Quartile Deviation} = \frac{Q_3 - Q_1}{Q_3 + Q_1} Coefficient of Quartile Deviation=88−2288+22=66110=0.6\text{Coefficient of Quartile Deviation} = \frac{88 - 22}{88 + 22} = \frac{66}{110} = 0.6
Expressing it as a percentage: Coefficient of Quartile Deviation in %=0.6×100=60\text{Coefficient of Quartile Deviation in } \% = 0.6 \times 100 = 60 Since the textbook represents the coefficient in percentage form: 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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