What this calculator does
The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage. It answers a question the standard deviation alone cannot: is this data more variable than that data, when the two are measured on different scales or in different units.
A standard deviation of 2.6 means nothing without context. Against a mean of 25 it is a coefficient of 10.4%, which is modest. Against a mean of 5 it would be 52%, which is very spread out. The division by the mean is what makes the measure comparable between a data set in dollars and one in kilograms.
The formula
The sample standard deviation, using the n−1 denominator, is divided by the mean and multiplied by 100. Because it divides by the mean, the measure is only meaningful for data on a ratio scale with a true zero and positive values. It breaks down when the mean is near zero, since a small denominator sends the result to infinity, and it is meaningless for data that can be negative.
| Term | Meaning |
|---|---|
| CV | Coefficient of variation: standard deviation as a percentage of the mean. |
| Relative variability | Spread judged against the size of the values, rather than in absolute units. |
| Ratio scale | A scale with a true zero, such as weight or income. Required for the CV to mean anything. |
| Sample standard deviation | Uses n−1 in the denominator, which corrects the bias in estimating a population from a sample. |
The inputs explained
| Field | What to enter |
|---|---|
| Data (comma or space separated) | Your data, comma or space separated. Values should be positive and on a ratio scale for the coefficient to be interpretable. |
When to use it
Comparing variability across units
Rainfall in millimetres and temperature in degrees cannot be compared by standard deviation, but they can by coefficient of variation.
Assessing measurement precision
Laboratory and manufacturing work often quotes precision as a CV, since it scales sensibly with the size of what is being measured.
Comparing investment volatility
Two assets with different average returns are compared on risk per unit of return, which is essentially what the CV expresses.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the coefficient of variation change with the data?
Data sets with very different spreads relative to their means.
| Data set | Coefficient of variation | Sample standard deviation | Mean |
|---|---|---|---|
| 100, 102, 98, 101, 99 | 1.58% | 1.581 | 100.000 |
| 23, 27, 25, 22, 29, 24 | 10.4% | 2.608 | 25.000 |
| 2, 4, 6, 8, 10 | 52.7% | 3.162 | 6.000 |
| 5, 50, 20, 80, 35 | 75.9% | 28.853 | 38.000 |
Questions
What is a good coefficient of variation?
It depends entirely on the field. Analytical chemistry might require under 5%, while biological or economic data is routinely above 30% without anything being wrong. There is no universal threshold, and any rule of thumb you see quoted is domain-specific.
When should I not use the coefficient of variation?
When the data can be negative or has no true zero, such as temperature in Celsius, and when the mean is close to zero. In both cases the division by the mean either changes sign or blows up, and the result is not interpretable.
Is the coefficient of variation the same as relative standard deviation?
Yes, the terms are used interchangeably. Relative standard deviation is the more common name in analytical chemistry and laboratory work; coefficient of variation is more common in statistics and economics.
Should I use the sample or population standard deviation?
The sample version, with n−1, if your data is a sample from a larger population, which it almost always is. This calculator uses the sample form. The difference matters most for small data sets and becomes negligible as n grows.
For the full set of summary statistics, see the descriptive statistics calculator. For standardising an individual value, see the z-score calculator.