Coefficient of Variation Calculator
Calculate the coefficient of variation: CV = (standard deviation / mean) × 100.
Compare variability between datasets with different units or scales.
The coefficient of variation (CV) measures relative variability by expressing standard deviation as a percentage of the mean. Unlike the standard deviation alone, which is in the same units as the data, the CV is a dimensionless number. That makes it the right tool for comparing spread across datasets that have different units or vastly different means.
The formula: CV = (σ ÷ μ) × 100
Where σ is the standard deviation and μ is the mean. The result is a percentage.
Why CV beats raw standard deviation for comparisons
Comparing the variability of stock returns (in percentages) to the variability of house prices (in dollars) using standard deviation alone is meaningless: the units don’t match. The CV normalizes the spread relative to the average, giving a fair comparison on the same scale.
Reference ranges
| CV | Interpretation |
|---|---|
| Below 15% | Low variability |
| 15% to 30% | Moderate variability |
| Above 30% | High variability |
These thresholds are general defaults. Specific fields use stricter ranges: a CV above 2% on an analytical chemistry validation is poor precision; a CV above 5% on a stock return is normal.
Worked example 1: test scores
A set of test scores has mean 75 and standard deviation 12. CV = (12 ÷ 75) × 100 = 16% Moderate variability. The standard deviation is 16% of the mean.
Worked example 2: comparing two investments
Investment A: mean return 8%, standard deviation 3%. CV = (3 ÷ 8) × 100 = 37.5% Investment B: mean return 15%, standard deviation 7%. CV = (7 ÷ 15) × 100 = 46.7%
Investment A has lower relative variability despite the smaller return. The volatility is more contained relative to the expected outcome. Risk-adjusted, A may actually be the steadier holding.
The limitations
The CV is only meaningful when the data is measured on a ratio scale with a true zero point. Don’t use it with interval-scale data like temperature in Celsius or Fahrenheit, because the mean can be zero or negative and the ratio becomes meaningless. Use Kelvin for temperature CVs.
CV also becomes unstable as the mean approaches zero. Small fluctuations in a tiny mean produce huge CVs that overstate real variability. If your mean is close to zero, the CV is not a useful summary.
Common applications
- Analytical chemistry: validating the precision of a measurement method
- Finance: comparing the risk-adjusted variability of different investments
- Biology: assessing measurement reproducibility across experiments
- Manufacturing: quality control across production lines or batches
- Climatology: comparing rainfall variability between regions with very different annual totals
Karl Pearson first defined the coefficient of variation in the late 1800s as part of his foundational work on statistical measures. It has stayed in active use because the underlying idea (normalize spread by central tendency) is robust across applications.