Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3187 of 473
All Questions

If mean and coefficient of variation of the marks of n\displaystyle n students is 20 and 80 respectively. What will be variance of them

Options

A256
B16
C25
DNone of these
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Correct Answer

✅ Option a — 256

All Options:

  • A256
  • B16
  • C25
  • DNone of these

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Detailed Solution & Explanation

**Given:** Mean xˉ=20\displaystyle \bar{x} = 20, CV = 80 **Step 1: Find SD using CV formula.** CV=σxˉ×100CV = \frac{\sigma}{\bar{x}} \times 100 80=σ20×10080 = \frac{\sigma}{20} \times 100 σ=80×20100=16\sigma = \frac{80 \times 20}{100} = 16 **Step 2: Find Variance.** σ2=162=256\sigma^2 = 16^2 = 256 Hence, **Option A** 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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