Descriptive statistics
Coefficient of Variation Calculator
The standard deviation as a share of the mean — spread you can compare across different scales and units.
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How to read this result
CV is unitless, and that is the entire point. A standard deviation of 5 kg cannot be compared with a standard deviation of 5 seconds. Divide each by its own mean and both become pure numbers that can sit in the same table.
Read it as a percentage of the level. CV = 18% means the typical deviation is about a fifth of the average value. Below 10% is tight, 10–30% is moderate, above 30% is highly variable — rough conventions, and worth calibrating against what is normal in your field.
It needs a ratio scale with a meaningful zero. Temperatures in Celsius, IQ scores centred at 100, and anything that can be negative all break it: the denominator is arbitrary, so the ratio is too. Weights, times, counts and prices are fine.
Near-zero means make it explode. As the mean approaches zero the CV grows without limit, so a large CV on data centred near zero says more about the denominator than about the spread.
The formula
- the standard deviation
- the mean
Also called the relative standard deviation. Use the population σ and μ when the data are the whole population.
Worked example
Comparing the variability of two very different measurements
Twenty daily customer counts: 18, 22, 25, 19, 31, 28, 24, 21, 27, 33, 26, 23, 29, 20, 35, 30, 22, 26, 24, 28. Their mean is 25.55 and their standard deviation 4.64. Is that more or less variable than a process with a mean of 2.4 kg and a standard deviation of 0.5 kg? The raw SDs are not comparable; the CVs are.
- Compute the mean and the standard deviation.mean = 25.55, s = 4.639
- Divide.4.639 / 25.55 = 0.1816
- Express as a percentage.CV = 18.2%
- Do the same for the other process.0.5 / 2.4 = 20.8%
Two quantities measured in entirely different units, compared in one number. That is the only thing the coefficient of variation is for, and it does it well.
Checked against R's sd(x)/mean(x).
The calculator above is loaded with these numbers by the Load the worked example button.
Assumptions, and when to use something else
A ratio scale with a true zero and a mean that is comfortably positive. Data that crosses zero makes the CV meaningless; data centred near zero makes it unstable.
It also inherits the standard deviation's sensitivity to outliers — a single extreme value inflates the numerator and can double the CV.
- You want spread in the original unitsStandard deviationThe absolute measure, in the data's own units.
- Outliers are inflating itRange and MADRobust measures of spread that a single extreme value cannot dominate.
- You are comparing two groups' variabilityLevene's testTests formally whether the spreads differ.
Questions people ask
What is a good coefficient of variation?
Field-dependent. In analytical chemistry a CV above 5% may fail a quality check; in biology 30% is unremarkable. Compare against the typical value for your own domain rather than against a universal threshold.
Can the coefficient of variation be negative?
Only if the mean is negative, and in that case the measure is not interpretable. This calculator uses the absolute value of the mean and warns you, because a CV on a scale that crosses zero is a number without a meaning.
Is CV the same as relative standard deviation?
Yes — RSD is the same quantity, and the term is more common in laboratory and analytical work. Both usually mean the sample version, expressed as a percentage.