Measures of Central Tendency and DispersionPYQ Sept 25Question 4173 of 473
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Coefficient of range of 84, 93, 53, 70, 82, 65 is

Options

A28.38
B27.39
C26.75
D29.31
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Correct Answer

✅ Option b — 27.39

All Options:

  • A28.38
  • B27.39
  • C26.75
  • D29.31

Detailed Solution & Explanation

Let us calculate the Coefficient of Range for the given set of observations:
84,93,53,70,82,6584, 93, 53, 70, 82, 65
1. **Identify the extreme values**:
- Largest value (L\displaystyle L) = 93\displaystyle 93
- Smallest value (S\displaystyle S) = 53\displaystyle 53
2. **Formula for Coefficient of Range**:
Coefficient of Range=L−SL+S×100\text{Coefficient of Range} = \frac{L - S}{L + S} \times 100
3. **Calculation**:
Substitute the values of L\displaystyle L and S\displaystyle S into the formula:
Coefficient of Range=93−5393+53×100\text{Coefficient of Range} = \frac{93 - 53}{93 + 53} \times 100
Coefficient of Range=40146×100\text{Coefficient of Range} = \frac{40}{146} \times 100
Coefficient of Range=4000146≈27.397\text{Coefficient of Range} = \frac{4000}{146} \approx 27.397
Rounding to two decimal places, we get 27.39\displaystyle 27.39.
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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