If sigma^2 = 100 & coefficient of variation = 20% then x

Option d: 50. Solution: We are given: - Variance: sigma^2 = 100 implies text{Standard Deviation } (sigma) = sqrt(100) = 10 - Coefficient of Variation (C.V.) = 20% The formula for the coefficient of variation is: C.V. = sigma/x-bar x 100 Substitute the given values: 20 = 10/x-bar x 100 20x-bar = 1000 implies x-bar = 50 Hence, Option D is the correct answer.

Central Tendency & DispersionPYQ June 19Question 3119 of 473

All Questions

If $\displaystyle \sigma^2 = 100$ & coefficient of variation $\displaystyle = 20\%$ then $\displaystyle x$

Options

\displaystyle 60

\displaystyle 70

\displaystyle 80

\displaystyle 50

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Correct Answer

✅ Option d — $\displaystyle 50$

All Options:

A $\displaystyle 60$
B $\displaystyle 70$
C $\displaystyle 80$
D $\displaystyle 50$

Detailed Solution & Explanation

We are given: - Variance:

\displaystyle \sigma^2 = 100 \implies \text{Standard Deviation } (\sigma) = \sqrt{100} = 10

- Coefficient of Variation (C.V.) =

\displaystyle 20\%

The formula for the coefficient of variation is:

C.V. = \frac{\sigma}{\bar{x}} \times 100

Substitute the given values:

20 = \frac{10}{\bar{x}} \times 100

20\bar{x} = 1000 \implies \bar{x} = 50

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

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If σ2=100\displaystyle \sigma^2 = 100σ2=100 & coefficient of variation =20%\displaystyle = 20\%=20% then x\displaystyle xx