Measures of Central Tendency and DispersionMCQPYQ June 22Question 3135 of 473
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Following are the wages of 8 workers $82, 96, 52, 75, 70, 65, 50, 70$. Find range and coefficient of range?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $46, 31.50$

All Options:

  • A$46, 32.70$
  • B$43, 31.50$
  • C$46, 31.50$
  • D$43, 32.70$

Detailed Solution & Explanation

**Given data:** 82, 96, 52, 75, 70, 65, 50, 70 **Step 1: Find Maximum and Minimum values.** L=max⁡=96,S=min⁡=50L = \max = 96, \quad S = \min = 50 **Step 2: Calculate Range.** Range=L−S=96−50=46Range=L−S=96−50=46\displaystyle \text{Range} = L - S = 96 - 50 = 46 **Step 3: Calculate Coefficient of Range.** Coefficient of Range=L−SL+S×100=96−5096+50×100Coefficient of Range=L−SL+S\displaystyle \text{Coefficient of Range} = \frac{L - S}{L + S} ×\displaystyle \times 100 = 96−5096+50\displaystyle \frac{96 - 50}{96 + 50} ×\displaystyle \times 100 =46146×100=0.3151×100≈31.50%= 46146\displaystyle \frac{46}{146} ×\displaystyle \times 100 = 0.3151 ×\displaystyle \times 100 ≈\displaystyle \approx 31.50\% **Result:** Range = 46, Coefficient of Range = 31.50 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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