Question

In a distribution if mean is 4 and coefficient of variation is 75%, then the variance is:

• A. 3
• B. 27
• C. 81
• D. 9

Hint:

Variance is the square of the standard deviation.

Answer 1

The Correct Option is D

Step 1: Concept
Coefficient of Variation (CV).

Step 2: Analysis
$CV = (\frac{\sigma}{\mu}) \times 100$.
Given $CV = 75$ and $\mu = 4$.

Step 3: Calculation
$75 = (\frac{\sigma}{4}) \times 100 \implies \sigma = \frac{75 \times 4}{100} = 3$.
Variance = $\sigma^2 = 3^2 = 9$.

Step 4: Conclusion
The variance is 9. Final Answer: (D)