Question

The coefficient of variation (C.V.) and the mean of a distribution are respectively 75 and 44. Then the standard deviation of the distribution is

• A. 30
• B. 31
• C. 32
• D. 33
• E. 35

Answer 1

The Correct Option is D

The coefficient of variation (C.V.) is defined as the ratio of the standard deviation (\( \sigma \)) to the mean (\( \mu \)) of the distribution, multiplied by 100: \[ \text{C.V.} = \frac{\sigma}{\mu} \times 100 \] We are given:
\( \text{C.V.} = 75 \)
\( \mu = 44 \)
Substitute these values into the formula for C.V: \[ 75 = \frac{\sigma}{44} \times 100 \] Solving for \( \sigma \) (standard deviation): \[ \sigma = \frac{75 \times 44}{100} = \frac{3300}{100} = 33 \]

The correct option is (D) : \(33\)

Answer 2

The coefficient of variation (C.V.) is defined as the ratio of the standard deviation (\(\sigma\)) to the mean (\(\mu\)), expressed as a percentage:

\(C.V. = \frac{\sigma}{\mu} \times 100\)

We are given that C.V. = 75 and the mean \(\mu = 44\). We want to find the standard deviation \(\sigma\).

Plugging in the given values, we have:

\(75 = \frac{\sigma}{44} \times 100\)

Solving for \(\sigma\), we get:

\(\sigma = \frac{75 \times 44}{100} = \frac{3300}{100} = 33\)

Therefore, the standard deviation of the distribution is 33.