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

Option d: 8.65%. Solution: Given: Variance = 12, Mean = 40 Step 1: Calculate SD. sigma = sqrt(12) = 2sqrt(3) approx 3.4641 Step 2: Calculate CV. CV = sigma/x-bar x 100 = 3.4641/40 x 100 approx 8.660% Closest to 8.65% (Option D). Hence, Option D is the correct answer.

Central Tendency & DispersionMTP June 2023 Series IQuestion 3198 of 473

All Questions

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

Options

\displaystyle 5.66\%

\displaystyle 6.66\%

\displaystyle 7.50\%

\displaystyle 8.65\%

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Correct Answer

✅ Option d — $\displaystyle 8.65\%$

All Options:

A $\displaystyle 5.66\%$
B $\displaystyle 6.66\%$
C $\displaystyle 7.50\%$
D $\displaystyle 8.65\%$

Detailed Solution & Explanation

**Given:** Variance = 12, Mean = 40 **Step 1: Calculate SD.**

\sigma = \sqrt{12} = 2\sqrt{3} \approx 3.4641

**Step 2: Calculate CV.**

CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{3.4641}{40} \times 100 \approx 8.660\%

Closest to

\displaystyle 8.65\%

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

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If the variance of given data is 12\displaystyle 1212, and their mean value is 40\displaystyle 4040, what is coefficient of variation (CV)?