If the variance of 5, 7, 9 and 11 is 4, then the coefficient of variation is:

Option b: 25. Solution: We are given the dataset: 5, 7, 9, 11. 1. Calculate the arithmetic mean (x-bar): x-bar = 5 + 7 + 9 + 11/4 = 32/4 = 8 2. We are given the variance is sigma^2 = 4. Thus, the standard deviation is: sigma = sqrt(4) = 2 3. Calculate the coefficient of variation (C.V.): C.V. = sigma/x-bar x 100 = 2/8 x 100 = 25% Hence, Option B is the correct answer.

If the variance of $5, 7, 9$ and $11$ is $4$, then the coefficient of variation is:

The correct answer is Option b: $25$. We are given the dataset: $5, 7, 9, 11$. 1. Calculate the arithmetic mean ($\bar{x}$): $$\bar{x} = \frac{5 + 7 + 9 + 11}{4} = \frac{32}{4} = 8$$ 2. We are given the variance is $\sigma^2 = 4$. Thus, the standard deviation is: $$\sigma = \sqrt{4} = 2$$ 3. Calculate the coefficient of variation (C.V.): $$C.V. = \frac{\sigma}{\bar{x}} \times 100 = \frac{2}{8} \times 100 = 25\%$$ Hence, **Option B** is the correct answer.

Central Tendency & DispersionPYQ Nov 18Question 3116 of 473

All Questions

If the variance of $\displaystyle 5, 7, 9$ and $\displaystyle 11$ is $\displaystyle 4$ , then the coefficient of variation is:

Options

\displaystyle 15

\displaystyle 25

\displaystyle 17

\displaystyle 19

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Correct Answer

✅ Option b — $\displaystyle 25$

All Options:

A $\displaystyle 15$
B $\displaystyle 25$
C $\displaystyle 17$
D $\displaystyle 19$

Detailed Solution & Explanation

We are given the dataset:

\displaystyle 5, 7, 9, 11

. 1. Calculate the arithmetic mean (

\displaystyle \bar{x}

\bar{x} = \frac{5 + 7 + 9 + 11}{4} = \frac{32}{4} = 8

2. We are given the variance is

\displaystyle \sigma^2 = 4

. Thus, the standard deviation is:

\sigma = \sqrt{4} = 2

3. Calculate the coefficient of variation (C.V.):

C.V. = \frac{\sigma}{\bar{x}} \times 100 = \frac{2}{8} \times 100 = 25\%

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

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If the variance of 5,7,9\displaystyle 5, 7, 95,7,9 and 11\displaystyle 1111 is 4\displaystyle 44, then the coefficient of variation is: