Coefficient of Variation Calculator

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The coefficient of variation (CV) is the standard deviation as a percent of the mean: CV = s ÷ x̄ × 100%. It lets you compare spread between data sets with different units or very different means.

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What do you have?

Data (separate with commas or spaces)

Data are a

Coefficient of variation

29.1%

The standard deviation is 29.1% of the mean.

Result
Count	8
Mean	18
Standard deviation	5.237229
Coefficient of variation	29.0957%
As a decimal	0.290957

Show steps

Mean = 144 ÷ 8 = 18.
Sum of squared deviations = 192; divide by n − 1 = 7 and take the square root: 5.237229.
CV = 5.237229 ÷ 18 × 100 = 29.0957%.

How to use the calculator

Choose raw data or summary values.
For raw data, paste the numbers and say whether they are a sample or the whole population.
Press Calculate to get the mean, standard deviation and CV.

Formula

Sample: CV = s ÷ x̄ × 100%
Population: CV = σ ÷ μ × 100%

For 10, 12, 23, 23, 16, 23, 21, 16 the mean is 18 and the sample standard deviation is 5.24, so CV = 5.24 ÷ 18 × 100 = 29.1%.

Why use the CV?

The standard deviation is in the same units as the data, so it cannot compare spread across different scales. Suppose mouse weights have SD 2 g with mean 20 g (CV 10%) and elephant weights have SD 300 kg with mean 5,000 kg (CV 6%). The elephants have the bigger SD, but relative to their size they vary less.

Data set	Mean	SD	CV
Mouse weight	20 g	2 g	10%
Elephant weight	5,000 kg	300 kg	6%
Lab test repeat	4.8 mmol/L	0.12 mmol/L	2.5%

When not to use it

Use the CV only for data on a ratio scale with a true zero, such as length, weight, time or money. It is meaningless for temperatures in °C or °F, where 0 is arbitrary, and it becomes unstable when the mean is close to 0.

Coefficient of variation practice questions

Test yourself with 6 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you calculate the coefficient of variation?

Divide the standard deviation by the mean and multiply by 100. With SD 3 and mean 60 the CV is 5%.

What is a good coefficient of variation?

It depends on the field. Lab methods often aim for a CV under 5% between repeat tests, while biological measurements commonly vary much more. Compare CVs within the same kind of data.

Should I use the sample or population standard deviation?

Use the sample formula (dividing by n − 1) when your data are a sample from a larger group, which is the usual case. Use the population formula only when you have every member of the group.

Can the CV be more than 100%?

Yes. When the standard deviation is larger than the mean, the CV is above 100%. This happens with data that have a long right tail, such as incomes.

Sources

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Effortless Math Team

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