What the coefficient of variation measures
The coefficient of variation (CV), also called the relative standard deviation (RSD), measures how large a dataset's spread is relative to its mean. Standard deviation alone tells you the absolute spread in the original units, but a standard deviation of 5 means something very different for values that average 10 than for values that average 10,000. The CV divides the standard deviation by the mean, cancelling the units and producing a single, scale-free percentage that lets you compare variability across datasets measured on completely different scales.
The formula
The coefficient of variation is the ratio of the standard deviation (σ) to the mean (μ), usually multiplied by 100 to express it as a percentage:
CV = σ / μ → CV% = (σ / μ) × 100
The mean is the sum of the values divided by their count. The standard deviation is the square root of the variance, where the variance is the average of the squared deviations from the mean. There are two variants of the standard deviation, and the choice matters for the CV:
- Population standard deviation divides the sum of squared deviations by n. Use it when your data covers the whole group you care about.
- Sample standard deviation divides by n − 1 (Bessel's correction). Use it when your data is a sample drawn from a larger population; it corrects the downward bias of the population formula on samples.
This calculator lets you pick either. For the same numbers the sample CV is a little larger, because dividing by n − 1 instead of n inflates the standard deviation.
A worked example
Take the dataset 12, 15, 18, 20, 22, 25, 28 (n = 7). The mean is (12 + 15 + 18 + 20 + 22 + 25 + 28) / 7 = 140 / 7 = 20. The squared deviations from 20 are 64, 25, 4, 0, 4, 25, 64, which sum to 186. The population variance is 186 / 7 ≈ 26.571, so σ ≈ 5.155. The coefficient of variation is 5.155 / 20 ≈ 0.2577, or about 25.77%. Using the sample standard deviation instead, the variance is 186 / 6 = 31, σ ≈ 5.568, and CV ≈ 27.84%.
Why it is useful
Because the CV is dimensionless, it answers questions absolute spread cannot. A lab can compare the precision of two assays that report in different units. An investor can compare the risk-per-unit-of-return of two assets with different price levels. A manufacturer can check whether a machined part's dimensional variability is acceptable relative to its target size, regardless of whether that target is millimetres or metres.
Common reference points
There is no universal cutoff, but some rules of thumb are widely used. In analytical chemistry a CV (RSD) under roughly 2–5% is often considered good precision for a repeated measurement. In finance, a lower CV of returns means less volatility per unit of return. As a loose interpretive guide, a CV below about 15% often reads as low relative variability, 15–30% as moderate, and above 30% as high — but the right threshold always depends on the field and the decision at hand.