Central Tendency & DispersionPYQ Dec 22Question 3140 of 473

If the variance of given data is 12, and their mean value is 40, what is coefficient of variation (CV)?

\displaystyle 5.66\%

\displaystyle 6.66\%

\displaystyle 7.50\%

\displaystyle 8.65\%

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Correct Answer

✅ Option d — $\displaystyle 8.65\%$

**Given:** Variance

\displaystyle = 12

, Mean

\displaystyle = 40

**Step 1: Find Standard Deviation.**

\sigma = \sqrt{\text{Variance}} = \sqrt{12} = 2\sqrt{3} \approx 3.464

**Step 2: Calculate CV.**

CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{3.464}{40} \times 100 = 8.66\%

This is closest to

\displaystyle 8.65\%

(Option D). **Exact calculation:**

\displaystyle \sqrt{12} = 2\sqrt{3}

CV = \frac{2\sqrt{3}}{40} \times 100 = \frac{\sqrt{3}}{0.2} = 5\sqrt{3} \approx 5 \times 1.7321 = 8.660\%

Hence, **Option D** is the correct answer.

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