What is Coefficient of Variation?
The Coefficient of Variation (CV), also known as Relative Standard Deviation (RSD), is a standardized measure of dispersion. It expresses the standard deviation as a percentage of the mean, making it useful for comparing variability across datasets with different units or scales.
Dataset A: Heights
Mean: 170 cm, SD: 10 cm
CV = 5.9%
Dataset B: Weights
Mean: 70 kg, SD: 10 kg
CV = 14.3%
Same SD (10), but CV reveals weights are relatively more variable
The CV Formula
Coefficient of Variation
CV = (σ / μ) × 100%
Where σ is the standard deviation and μ is the mean. For sample data, use s and x̄ respectively.
Calculation Example
Dataset: 12, 15, 14, 18, 11
- Mean (x̄) = 14
- Standard Deviation (s) = 2.74
- CV = (2.74 / 14) × 100% = 19.6%
When to Use CV
Use CV When:
- Comparing datasets with different units
- Comparing datasets with very different means
- Data is ratio-scale (true zero point)
- Assessing consistency in lab measurements
- Financial analysis (comparing volatility)
Use SD When:
- Datasets have same units and similar means
- Data is interval-scale (like temperature)
- Mean is zero or close to zero
- You need absolute spread information
Practical Examples
Laboratory Quality Control
In analytical chemistry, a CV below 10% is often considered acceptable for precision. Highly precise methods may achieve CV < 5%.
| Stock | Return | SD | CV |
|---|---|---|---|
| Stock A | 8% | 4% | 50% |
| Stock B | 12% | 9% | 75% |
Stock A has lower CV = more return per unit of risk
Limitations of CV
Important Limitations
- Undefined when mean = 0: Division by zero makes CV meaningless
- Problematic with negative values: Can produce misleading results
- Not for interval scales: Temperature in Celsius/Fahrenheit has arbitrary zero
Further Reading
Sources
References and further authoritative reading used in preparing this article.