Coefficient of Variation Calculator
Relative dispersion: SD / mean
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Coefficient of variation from a data set
Dividing the standard deviation by the mean makes spread unit-free, which is what the coefficient of variation is for: it is the figure to compare when two data sets sit on different scales or have very different averages.
The coefficient of variation is 20.20%, which says the typical deviation is about a fifth of the average.
The formula
CV = (standard deviation ÷ mean) × 100
Mean = 70 ÷ 5 = 14. Deviations from the mean are −4, −2, 0, 2, 4, and their squares sum to 40, so the variance is 40 ÷ 5 = 8 and σ = 2.828. Then 2.828 ÷ 14 × 100 = 20.20%.
Worked examples
10, 12, 14, 16, 18 → mean 14, σ 2.83, CV 20.20%
100, 102, 98 → mean 100, σ 1.63, CV 1.63%
5, 10, 15 → mean 10, σ 4.08, CV 40.82%
2, 4, 6, 8, 10 → mean 6, σ 2.83, CV 47.14%
50, 50, 50 → mean 50, σ 0, CV 0%
Why divide by the mean at all
Standard deviation carries the units of the data, so a spread of 2.8 means something very different on a set averaging 14 than on one averaging 1,400. Dividing by the mean removes the scale and leaves a pure ratio, which is what lets you compare variability across measurements that are not in the same units — weight consistency against delivery times, or rainfall across two regions with different totals.
Where it misleads
- Means near zero. A mean close to zero inflates the CV without limit, and a mean of exactly zero makes it undefined.
- Data with negative values. If values can go below zero, the ratio loses its meaning and a sign change flips the result.
- Population or sample. Dividing by n gives 20.20% here; dividing by n − 1 gives 22.59%. State which you used.
- Ratios and proportions. A CV computed on percentages or indices is hard to interpret because the scale is already artificial.
- Comparing different shapes. A CV of 20% can come from one outlier or from evenly spread data — look at the values, not just the summary.
Report the mean and standard deviation alongside it. The CV is a comparison aid, not a description you can read on its own.
Frequently Asked Questions
What is the coefficient of variation for 10, 12, 14, 16, 18?
20.20%, from a standard deviation of 2.83 and a mean of 14.
What does a CV actually tell me?
How large the spread is relative to the average, which makes variability comparable between data sets with different scales or units.
Is a high CV good or bad?
Neither on its own. Low CV means consistency; whether consistency is desirable depends on what is being measured.
Why does my CV differ from another calculator?
Usually because of the divisor: population standard deviation divides by n, sample standard deviation by n − 1. This tool uses the population form.
Can the CV be used when the mean is zero?
No. Division by zero makes it undefined, and a mean near zero produces enormous, meaningless percentages.
What is a typical CV?
There is no universal threshold. In analytical chemistry a few percent is normal; in biology or finance 20–30% is unremarkable.
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