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-bar x 100 60 = 12/x-bar x 100 Step 2: Solve for Mean. x-bar = 12 x 100/60 = 1200/60 = 20 Hence, Option C is the correct answer.

Central Tendency & DispersionMTP 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.

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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