Measures of Variance
The Coefficient of Variation
Learning Objectives
Calculate and understand the coefficient of variation.
The Coefficient of Variation (CV):
- Is the best metric to compare two different data sets with fairly different means
- It measures the standard deviation, [latex]s[/latex] or [latex]\sigma[/latex] as a percent of the mean
The SAMPLE coefficient of variation is defined as:
\[ CV_{sample} = \frac{s}{\bar{x}} \times 100 \% \]
The POPULATION coefficient of variation is defined as:
\[ CV_{population} = \frac{\sigma}{\mu} \times 100 \% \]
Example 8.1 – Sunita and Sanjay’s Coefficients of Variation
Let us re-examine how Sunita and Sanjay’s grades are distributed. We calculated the following metrics in previous sections for the distribution of their grades:
| Name | Mean | Median | Range | St Dev | Variance |
|---|---|---|---|---|---|
| Sunita | 81 | 80 | 3 | 1.41421 | 2 |
| Sanjay | 81 | 80 | 51 | 20.6398 | 426 |
We can then calculate the coefficient of variation for both Sunita and Sanjay from the above metrics:
- Sunita’s coefficient of variation is:
\[ CV_{Sunita} = \frac{1.41421}{81} \times 100 \% = 1.75\% \]
- Sanjay’s coefficient of variation is:
\[ CV_{Sanjay} = \frac{20.6398}{81} \times 100 \% = 25.48\%\]
Click here to download the Excel spreadsheet with the above calculations.
Key Takeaways
Key Takeaways: The Coefficient of Variation
- The coefficient of variation should be used when comparing populations with very different means.
- It measures the standard deviation as a percent of the mean.
- It is expressed as a percent (and not usually as a decimal).
- It is often used in business and finance (ex: when comparing investments).
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