Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 3198 of 473
All Questions

If the variance of given data is 12\displaystyle 12, and their mean value is 40\displaystyle 40, what is coefficient of variation (CV)?

Options

A5.66%\displaystyle 5.66\%
B6.66%\displaystyle 6.66\%
C7.50%\displaystyle 7.50\%
D8.65%\displaystyle 8.65\%
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Correct Answer

✅ Option d — 8.65%\displaystyle 8.65\%

All Options:

  • A5.66%\displaystyle 5.66\%
  • B6.66%\displaystyle 6.66\%
  • C7.50%\displaystyle 7.50\%
  • D8.65%\displaystyle 8.65\%

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Detailed Solution & Explanation

**Given:** Variance = 12, Mean = 40 **Step 1: Calculate SD.** σ=12=23≈3.4641\sigma = \sqrt{12} = 2\sqrt{3} \approx 3.4641 **Step 2: Calculate CV.** CV=σxˉ×100=3.464140×100≈8.660%CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{3.4641}{40} \times 100 \approx 8.660\% Closest to 8.65%\displaystyle 8.65\% (Option D). Hence, **Option D** 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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