Measures of Central Tendency and DispersionMCQPYQ July 21Question 3133 of 473
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If the numbers are 5,1,8,7,2\displaystyle 5, 1, 8, 7, 2 then the coefficient of variation is:

Options

A56.13%\displaystyle 56.13\%
B59.13%\displaystyle 59.13\%
C48.13%\displaystyle 48.13\%
D44.13%\displaystyle 44.13\%
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Correct Answer

✅ Option b — 59.13%\displaystyle 59.13\%

All Options:

  • A56.13%\displaystyle 56.13\%
  • B59.13%\displaystyle 59.13\%
  • C48.13%\displaystyle 48.13\%
  • D44.13%\displaystyle 44.13\%

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Detailed Solution & Explanation

**Given data:** 5, 1, 8, 7, 2; n=5\displaystyle n = 5 **Step 1: Calculate Mean.** xˉ=5+1+8+7+25=235=4.6\bar{x} = \frac{5+1+8+7+2}{5} = \frac{23}{5} = 4.6 **Step 2: Calculate deviations squared.** xi(xi−xˉ)(xi−xˉ)250.40.161−3.612.9683.411.5672.45.762−2.66.76\begin{array}{|c|c|c|} \hline x_i & (x_i - \bar{x}) & (x_i - \bar{x})^2 \\ \hline 5 & 0.4 & 0.16 \\ 1 & -3.6 & 12.96 \\ 8 & 3.4 & 11.56 \\ 7 & 2.4 & 5.76 \\ 2 & -2.6 & 6.76 \\ \hline \end{array} **Step 3: Calculate Variance.** σ2=0.16+12.96+11.56+5.76+6.765=37.25=7.44\sigma^2 = \frac{0.16+12.96+11.56+5.76+6.76}{5} = \frac{37.2}{5} = 7.44 **Step 4: Calculate SD.** σ=7.44≈2.728\sigma = \sqrt{7.44} \approx 2.728 **Step 5: Calculate CV.** CV=σxˉ×100=2.7284.6×100≈59.3%CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{2.728}{4.6} \times 100 \approx 59.3\% This is closest to 59.13%\displaystyle 59.13\%. 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.

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