StatReason

Coefficient of Variation Calculator

Find the standard deviation as a percentage of the mean, useful for comparing variability across datasets with different units or scales.

Values should be on a true ratio scale (a meaningful zero), such as weight, price, or time.

What this answers

The coefficient of variation answers "how large is the spread relative to the average size of the values?" A standard deviation of 5 means something very different for a dataset averaging 10 than one averaging 1,000. Expressing spread as a percentage of the mean makes variability comparable across datasets with completely different units or scales, something the raw standard deviation alone cannot do.

How it is calculated

The coefficient of variation is the sample standard deviation divided by the absolute value of the mean, usually expressed as a percentage. It requires a true ratio scale, meaning zero genuinely means "none" (a weight, a price, a duration), since the result is meaningless or misleading on an interval scale where zero is arbitrary, such as temperature in Celsius or Fahrenheit.

Worked example

For the values 2, 4, and 6: the mean is 4 and the sample standard deviation is 2, so the coefficient of variation is 2 divided by 4, exactly 50%. That means this dataset's spread equals half of its average value, a genuinely large relative variability regardless of the units involved.

Assumption audit

Calculated from your data: the mean, sample standard deviation, and whether the mean is at or near zero, which would make the ratio unstable or undefined.
Evidence to review: a warning appears below the result whenever the mean is small relative to the standard deviation, since small denominators make the CV highly sensitive to tiny changes in the mean.
You must verify: that your data genuinely lives on a ratio scale with a meaningful zero point. Applying CV to an interval-scale variable (like a temperature in degrees) produces a number that depends arbitrarily on which zero point that scale uses.

Common mistakes

Comparing the raw standard deviation of two datasets with very different average magnitudes is a common error the CV exists to fix: a standard deviation of $500 sounds large next to one of $5, but if the first dataset averages $50,000 and the second averages $10, the second is actually far more variable in relative terms. Comparing CVs directly avoids that scale illusion.

Limitations

The coefficient of variation is undefined when the mean is exactly zero, and unstable when the mean is close to zero relative to the spread. It should not be applied to data that can naturally take both positive and negative values around a mean near zero, and it should never be used to compare variability across two variables measured on genuinely different kinds of scales just because both happen to produce a percentage.