If mean and coefficient of variation of the marks of 10 students is 20 and 80 respectively. What will be the variance of them?

Option a: 256. Solution: Given: Mean x = 20 , CV = 80 Step 1: Find SD. CV = sigma/x × 100 80 = sigma/20 × 100 sigma = 80 × 20/100 = 16 Step 2: Find Variance. sigma2 = 162 = 256 Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IQuestion 3201 of 473

All Questions

If mean and coefficient of variation of the marks of $\displaystyle 10$ students is $\displaystyle 20$ and $\displaystyle 80$ respectively. What will be the variance of them?

Options

\displaystyle 256

\displaystyle 16

\displaystyle 25

DNone of these

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Correct Answer

✅ Option a — $\displaystyle 256$

All Options:

A $\displaystyle 256$
B $\displaystyle 16$
C $\displaystyle 25$
DNone of these

Detailed Solution & Explanation

**Given:** Mean

\displaystyle \bar{x} = 20

, CV = 80 **Step 1: Find SD.**

CV = \frac{\sigma}{\bar{x}} \times 100

80 = \frac{\sigma}{20} \times 100

\sigma = \frac{80 \times 20}{100} = 16

**Step 2: Find Variance.**

\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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If mean and coefficient of variation of the marks of 10\displaystyle 1010 students is 20\displaystyle 2020 and 80\displaystyle 8080 respectively. What will be the variance of them?