Question

The range of Coefficient of Variation (CV) is:

• A. \(-1 \leq \text{CV} \leq 1\)
• B. \(\text{CV} \geq 0\)
• C. \(\text{CV} \leq 0\)
• D. \(-\infty \leq \text{CV} \leq \infty\)

Hint:

Exam Tip:

• CV is a relative measure of dispersion.
• It is unitless.
• CV \(\ge 0\) for positive means.
• It is not defined when the mean is zero.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Coefficient of Variation (CV) is defined as: \[ \text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100 \]

Step 2: Key Properties:
Since standard deviation is always non-negative and mean can be positive or negative:
• If mean \(> 0\), CV is positive.
• If mean \(< 0\), CV is negative.
• If mean \(= 0\), CV is undefined. However, in most practical applications, the mean is positive, so CV is positive.
The CV is always non-negative if we consider the absolute value.
The range of CV is \(\text{CV} \geq 0\) when mean is positive.

Step 3: Analyzing the Options:

• (A) \(-1 \leq \text{CV} \leq 1\): False.
• (B) \(\text{CV} \geq 0\): True.
• (C) \(\text{CV} \leq 0\): False.
• (D) \(-\infty \leq \text{CV} \leq \infty\): False.

Step 4: Final Answer:
Therefore, option (B) is correct.