If mean and coefficient of variation of the marks of 10 students is 20 and 80 respectively. What will be the variance of them?

Option a: 256. Solution: Given: Mean x-bar = 20, CV = 80 Step 1: Find SD. CV = sigma/x-bar x 100 80 = sigma/20 x 100 sigma = 80 x 20/100 = 16 Step 2: Find Variance. sigma^2 = 16^2 = 256 Hence, Option A is the correct answer.

Central Tendency & DispersionMTP Dec 2023 Series IQuestion 3201 of 473

All Questions

If mean and coefficient of variation of the marks of $\displaystyle 10$ students is $\displaystyle 20$ and $\displaystyle 80$ respectively. What will be the variance of them?

Options

\displaystyle 256

\displaystyle 16

\displaystyle 25

DNone of these

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Correct Answer

✅ Option a — $\displaystyle 256$

All Options:

A $\displaystyle 256$
B $\displaystyle 16$
C $\displaystyle 25$
DNone of these

Detailed Solution & Explanation

**Given:** Mean

\displaystyle \bar{x} = 20

, CV = 80 **Step 1: Find SD.**

CV = \frac{\sigma}{\bar{x}} \times 100

80 = \frac{\sigma}{20} \times 100

\sigma = \frac{80 \times 20}{100} = 16

**Step 2: Find Variance.**

\sigma^2 = 16^2 = 256

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

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If mean and coefficient of variation of the marks of 10\displaystyle 1010 students is 20\displaystyle 2020 and 80\displaystyle 8080 respectively. What will be the variance of them?