If mean = 200 and variance = 80 . Find coefficient of variation.

Option b: 4.47. Solution: We are given: - Mean = 200 - Variance = 80 Standard Deviation (sigma) = sqrt(80) ≈ 8.94 The coefficient of variation (C.V.) is calculated as: C.V. = sigma/Mean × 100 = 8.94/200 × 100 = 4.47% Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3126 of 473

All Questions

If mean $\displaystyle = 200$ and variance $\displaystyle = 80$ . Find coefficient of variation.

Options

\displaystyle 2.56

\displaystyle 4.47

\displaystyle 32

\displaystyle 0.32

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Correct Answer

✅ Option b — $\displaystyle 4.47$

All Options:

A $\displaystyle 2.56$
B $\displaystyle 4.47$
C $\displaystyle 32$
D $\displaystyle 0.32$

Detailed Solution & Explanation

We are given: - Mean =

\displaystyle 200

- Variance =

\displaystyle 80 \implies \text{Standard Deviation } (\sigma) = \sqrt{80} \approx 8.94

The coefficient of variation (C.V.) is calculated as:

C.V. = \frac{\sigma}{\text{Mean}} \times 100 = \frac{8.94}{200} \times 100 = 4.47\%

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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If mean =200\displaystyle = 200=200 and variance =80\displaystyle = 80=80. Find coefficient of variation.