Measures of Central Tendency and DispersionMCQMTP Nov 21Question 3181 of 473
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If the variance of x=148.6\displaystyle x = 148.6 and mean of x=40\displaystyle x = 40, then the coefficient of variation is

Options

A37.15
B30.48
C33.75
DNone of these
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Correct Answer

✅ Option b — 30.48

All Options:

  • A37.15
  • B30.48
  • C33.75
  • DNone of these

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Detailed Solution & Explanation

**Given:** Variance =148.6\displaystyle = 148.6, Mean =40\displaystyle = 40 **Step 1: Calculate SD.** σ=148.6≈12.19\sigma = \sqrt{148.6} \approx 12.19 **Step 2: Calculate CV.** CV=σxˉ×100=12.1940×100≈30.48%CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{12.19}{40} \times 100 \approx 30.48\% **Exact computation:** 148.6=12.1906...\displaystyle \sqrt{148.6} = 12.1906... CV=12.190640×100=30.48%CV = \frac{12.1906}{40} \times 100 = 30.48\% 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.

Key Concepts to Understand

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

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