Question

For a random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the coefficient of variation is:

• A. \(\frac{\mu}{\sigma} \times 100\)
• B. \(\frac{\sigma}{\mu} \times 100\)
• C. \(\frac{\sigma^2}{\mu} \times 100\)
• D. \(\frac{\mu}{\sigma^2} \times 100\)

Hint:

Coefficient of variation = \(\frac{\text{Standard Deviation}}{\text{Mean}} \times 100\).
It is used to compare the variability of two or more datasets.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The coefficient of variation (CV) is a measure of relative variability.
It is defined as the ratio of the standard deviation to the mean, expressed as a percentage.

Step 2: Key Formula or Approach:
\[ CV = \frac{\sigma}{\mu} \times 100%. \]

Step 3: Detailed Explanation:
The coefficient of variation is useful for comparing variability between datasets with different means.
It is dimensionless.
Option (A) is the inverse.
Option (C) uses variance instead of standard deviation.
Option (D) is also incorrect.
Thus, the correct answer is (B).
For example, if mean = 50 and standard deviation = 5, CV = 10%.