If the variance of 5, 7, 9 and 11 is 4 , then the coefficient of variation is:

Option b: 25. Solution: We are given the dataset: 5, 7, 9, 11 . 1. Calculate the arithmetic mean ( x ): x = 5 + 7 + 9 + 11/4 = 32/4 = 8 2. We are given the variance is sigma2 = 4 . Thus, the standard deviation is: sigma = sqrt(4) = 2 3. Calculate the coefficient of variation (C.V.): C.V. = sigma/x × 100 = 2/8 × 100 = 25% Hence, Option B is the correct answer.

If the variance of $5, 7, 9$ and $11$ is $4$, then the coefficient of variation is:

The correct answer is Option b: $25$. We are given the dataset: $5, 7, 9, 11$. 1. Calculate the arithmetic mean ($\bar{x}$): $$\bar{x} = \frac{5 + 7 + 9 + 11}{4} = \frac{32}{4} = 8$$ 2. We are given the variance is $\sigma^2 = 4$. Thus, the standard deviation is: $$\sigma = \sqrt{4} = 2$$ 3. Calculate the coefficient of variation (C.V.): $$C.V. = \frac{\sigma}{\bar{x}} \times 100 = \frac{2}{8} \times 100 = 25\%$$ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 3116 of 473

All Questions

If the variance of $\displaystyle 5, 7, 9$ and $\displaystyle 11$ is $\displaystyle 4$ , then the coefficient of variation is:

Options

\displaystyle 15

\displaystyle 25

\displaystyle 17

\displaystyle 19

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Correct Answer

✅ Option b — $\displaystyle 25$

All Options:

A $\displaystyle 15$
B $\displaystyle 25$
C $\displaystyle 17$
D $\displaystyle 19$

Detailed Solution & Explanation

We are given the dataset:

\displaystyle 5, 7, 9, 11

. 1. Calculate the arithmetic mean (

\displaystyle \bar{x}

\bar{x} = \frac{5 + 7 + 9 + 11}{4} = \frac{32}{4} = 8

2. We are given the variance is

\displaystyle \sigma^2 = 4

. Thus, the standard deviation is:

\sigma = \sqrt{4} = 2

3. Calculate the coefficient of variation (C.V.):

C.V. = \frac{\sigma}{\bar{x}} \times 100 = \frac{2}{8} \times 100 = 25\%

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 the variance of 5,7,9\displaystyle 5, 7, 95,7,9 and 11\displaystyle 1111 is 4\displaystyle 44, then the coefficient of variation is: