Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3128 of 473
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Coefficient of variation is $80$. Mean is $20$. Find variance:

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

✅ Option b — $256$

All Options:

  • A$640$
  • B$256$
  • C$16$
  • D$250$

Detailed Solution & Explanation

**Given:** Coefficient of Variation (CV) = 80, Mean xˉ\displaystyle xˉ\displaystyle \bar{x} = 20 **Step 1: Recall the formula for CV.** CV=σxˉ×100CV = σxˉ\displaystyle \frac{\sigma}{\bar{x}} ×\displaystyle \times 100 where σ\displaystyle σ\displaystyle \sigma = Standard Deviation. **Step 2: Substitute the given values.** 80=σ20×10080 = σ20\displaystyle \frac{\sigma}{20} ×\displaystyle \times 100 **Step 3: Solve for σ\displaystyle σ\displaystyle \sigma.** σ=80×20100=1600100=16\displaystyle \sigma = \frac{80 ×\displaystyle \times 20}{100} = 1600100=16\displaystyle \frac{1600}{100} = 16 **Step 4: Find Variance.** Variance=σ2=(16)2=256Variance=σ2\displaystyle \text{Variance} = \sigma^2 = (16)^2 = 256 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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