Central Tendency & DispersionPYQ 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\%

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.

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