Measures of Central Tendency and DispersionPYQ May 25Question 4073 of 473
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The monthly profit/loss for six months of the firm is as under: January ₹ 1,000, February ₹ 900, March ₹ 0, April ₹ -200, May ₹ -400, June ₹ 2,000. The co-efficient range of the above data is

Options

A122
B150
C33.33
D55.55
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Correct Answer

✅ Option b — 150

All Options:

  • A122
  • B150
  • C33.33
  • D55.55

Detailed Solution & Explanation

First, let us identify the maximum (largest) and minimum (smallest) values in the given dataset:
Data: {1000,900,0,−200,−400,2000}\text{Data: } \{1000, 900, 0, -200, -400, 2000\} - Largest value (L\displaystyle L) = 2000\displaystyle 2000
- Smallest value (S\displaystyle S) = −400\displaystyle -400

The coefficient of range is given by the formula:
Coefficient of Range=L−SL+S×100\text{Coefficient of Range} = \frac{L - S}{L + S} \times 100 Substituting L=2000\displaystyle L = 2000 and S=−400\displaystyle S = -400:
Coefficient of Range=2000−(−400)2000+(−400)×100\text{Coefficient of Range} = \frac{2000 - (-400)}{2000 + (-400)} \times 100 Coefficient of Range=2000+4002000−400×100\text{Coefficient of Range} = \frac{2000 + 400}{2000 - 400} \times 100 Coefficient of Range=24001600×100=32×100=150\text{Coefficient of Range} = \frac{2400}{1600} \times 100 = \frac{3}{2} \times 100 = 150
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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