Coefficient of Variation
Paste a dataset to get the coefficient of variation — the standard deviation as a percentage of the mean.
The coefficient of variation (CV) measures relative variability — the standard deviation expressed as a percentage of the mean: CV = SD ÷ mean × 100. Because it is unitless, it lets you compare the spread of datasets measured on different scales. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population SD is 2, so CV = 40%.
What the coefficient of variation tells you
Standard deviation alone can mislead: an SD of 5 is tiny on a scale that averages 1,000 and enormous on one that averages 10. The coefficient of variation fixes this by dividing the standard deviation by the mean, turning spread into a relative, unitless percentage. A CV of 40% means the standard deviation is 40% of the average value. Because the units cancel, you can compare the variability of test scores, prices, and reaction times side by side — something raw standard deviations can’t do.
use the sample SD (÷ n − 1) or population SD (÷ n) as appropriate
Worked example
Eight values: 2, 4, 4, 4, 5, 5, 7, 9, using the population standard deviation.
- 1 Find the mean. (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) ÷ 8 = 40 ÷ 8 = 5.
- 2 Find the standard deviation. The squared deviations sum to 32; population SD = √(32 ÷ 8) = √4 = 2.
- 3 Divide SD by the mean, then × 100. 2 ÷ 5 = 0.4, and 0.4 × 100 = 40%.
A rough guide to CV values
Interpretation is context-dependent — a “high” CV in one field is normal in another.
| CV | Relative spread | Reading |
|---|---|---|
| < 15% | Low | Values cluster tightly around the mean |
| 15% – 30% | Moderate | A typical, middling amount of spread |
| > 30% | High | Values are widely dispersed relative to the mean |
Interpreting and using the result
It compares spread across scales. The whole point of the CV is to compare variability between datasets with different units or very different means — heights in centimetres versus weights in kilograms, for example. Standard deviation can’t make that comparison; the CV can.
It breaks down near zero. Because you divide by the mean, the CV becomes unstable when the mean is close to zero — tiny changes in the mean swing it wildly — and it is undefined when the mean is exactly 0.
It needs a meaningful zero. The CV assumes a ratio scale with a true zero and positive values. It is not meaningful for data that can be negative (like temperatures in °C or profit-and-loss figures), where the mean may sit near or below zero.