Question

Ratio of the sample standard deviation to the sample mean
[Question ID = 1431]

• A. Standard error
• B. Co-efficient of variation
• C. Mean deviation
• D. Variance

Hint:

Remember: CV = (SD Mean) $\times$ It is expressed as a percentage. A lower CV indicates less variability and more consistency in the data set.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the name of the statistical measure that expresses the standard deviation as a percentage of the mean.
Key Formula or Approach:
The formula for the coefficient of variation (CV) is:
\[ CV = \left( \frac{\text{Standard Deviation } (\sigma)}{\text{Mean } (\mu)} \right) \times 100 \]

Step 2: Detailed Explanation:

• Definition: The Coefficient of Variation (CV) is a unitless measure of relative variability. It allows researchers to compare the degree of variation between data sets that have different units or widely different means.

• Significance: In fisheries biology, if you want to compare the variability in length (measured in cm) with the variability in weight (measured in grams), you cannot use standard deviation directly because the units differ. CV provides a normalized comparison.

• Other Options:
- Standard error: $\frac{\sigma}{\sqrt{n}}$. It measures the precision of the mean.
- Variance: $\sigma^2$. The square of the standard deviation.
- Mean deviation: The average of absolute differences from the mean.

Step 3: Final Answer:
The ratio described is the Coefficient of variation.