If the coefficient of variation and standard deviation are 60 and 12 respectively, then the arithmetic mean of the distribution is

Option c: 20. Solution: Given: CV = 60, SD ( sigma ) = 12 Step 1: Use CV formula. CV = sigma/x × 100 60 = 12/x × 100 Step 2: Solve for Mean. x = 12 × 100/60 = 1200/60 = 20 Hence, Option C is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 3195 of 473

All Questions

If the coefficient of variation and standard deviation are $\displaystyle 60$ and $\displaystyle 12$ respectively, then the arithmetic mean of the distribution is

Options

\displaystyle 40

\displaystyle 36

\displaystyle 20

\displaystyle 19

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Correct Answer

✅ Option c — $\displaystyle 20$

All Options:

A $\displaystyle 40$
B $\displaystyle 36$
C $\displaystyle 20$
D $\displaystyle 19$

Detailed Solution & Explanation

**Given:** CV = 60, SD (

\displaystyle \sigma

) = 12 **Step 1: Use CV formula.**

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

60 = \frac{12}{\bar{x}} \times 100

**Step 2: Solve for Mean.**

\bar{x} = \frac{12 \times 100}{60} = \frac{1200}{60} = 20

Hence, **Option C** 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

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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If the coefficient of variation and standard deviation are 60\displaystyle 6060 and 12\displaystyle 1212 respectively, then the arithmetic mean of the distribution is