Coefficient of variation is 80. Mean is 20. Find variance:

Option b: 256. Solution: Given: Coefficient of Variation (CV) = 80, Mean x-bar = 20 Step 1: Recall the formula for CV. CV = sigma/x-bar x 100 where sigma = Standard Deviation. Step 2: Substitute the given values. 80 = sigma/20 x 100 Step 3: Solve for sigma. sigma = 80 x 20/100 = 1600/100 = 16 Step 4: Find Variance. text{Variance} = sigma^2 = (16)^2 = 256 Hence, Option B is the correct answer.

Central Tendency & DispersionPYQ Nov. 19Question 3128 of 473

All Questions

Coefficient of variation is $\displaystyle 80$ . Mean is $\displaystyle 20$ . Find variance:

Options

\displaystyle 640

\displaystyle 256

\displaystyle 16

\displaystyle 250

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Correct Answer

✅ Option b — $\displaystyle 256$

All Options:

A $\displaystyle 640$
B $\displaystyle 256$
C $\displaystyle 16$
D $\displaystyle 250$

Detailed Solution & Explanation

**Given:** Coefficient of Variation (CV) = 80, Mean

\displaystyle \bar{x}

= 20 **Step 1: Recall the formula for CV.**

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

where

\displaystyle \sigma

= Standard Deviation. **Step 2: Substitute the given values.**

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

**Step 3: Solve for

\displaystyle \sigma

.**

\sigma = \frac{80 \times 20}{100} = \frac{1600}{100} = 16

**Step 4: Find Variance.**

\text{Variance} = \sigma^2 = (16)^2 = 256

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

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Coefficient of variation is 80\displaystyle 8080. Mean is 20\displaystyle 2020. Find variance: