What the coefficient of variation is
The CV is the SD divided by the mean, usually shown as a percentage: CV = s / x̄ × 100%. It expresses spread relative to size, which lets you compare variability across different units or scales. See the coefficient of variation explained.
Worked example
Are people more variable in height or in weight? Five heights have mean 170 cm and SD 7.91, so the CV is 4.7%. Five weights have mean 68 kg and SD 11.60, so the CV is 17.1%. The SDs cannot be compared directly because their units differ, but the CVs show weight is far more variable in relative terms.
When not to use it
- Means near zero: the CV explodes and becomes meaningless.
- Data without a true zero: temperature in °C gives one CV and in °F another for the same weather.
- Negative values: a mean can be close to zero even with large values.
The bias-adjusted version multiplies by (1 + 1/(4n)), which matters only for small samples. Results match SciPy’s variation with ddof=1.
Frequently asked questions
How do you calculate the coefficient of variation?
Divide the standard deviation by the mean and multiply by 100%.
What is a good coefficient of variation?
It depends on the field. In lab assays, under 10% is often considered good. There is no universal cut-off.
Can the CV be above 100%?
Yes, when the SD is larger than the mean. This is common for strongly right-skewed data.