Coefficient Of Variation Calculator

What the coefficient of variation calculator does

The coefficient of variation, or CV, measures spread relative to the average, rather than in absolute terms. It is the standard deviation divided by the mean, which turns a spread into a proportion of the size of the numbers. This calculator works it out from your data, and shows the mean and standard deviation behind it.

Because it has no units, the CV lets you compare how variable two data sets are even when they are measured on completely different scales. Below is how it works and why that matters.

How to use it

1. Enter your numbers in the box, separated by commas, spaces, or line breaks.
2. Press Calculate for the coefficient of variation along with the mean and standard deviation, or Reset to clear it.

How the coefficient of variation is worked out

It is one division. Take the standard deviation of your data and divide it by the mean:

Coefficient of variation = standard deviation ÷ mean

This calculator uses the population standard deviation and reports the CV as a plain ratio, so a result of 0.4 means the spread is 40 percent of the mean. To read it as a percentage, just multiply by 100. Because you are dividing a spread by an average that is in the same units, those units cancel, which is what leaves the CV as a pure, unitless number.

Why it lets you compare across scales

A standard deviation on its own cannot be compared between different kinds of data. A spread of ten centimetres in people's heights and a spread of ten kilograms in their weights are both "ten", but they mean very different things, because heights and weights sit on different scales.

The coefficient of variation fixes that by measuring each spread against its own average. Ten centimetres against an average height of 170 is a CV of about 0.06, while ten kilograms against an average weight of 70 is a CV of about 0.14. Now the two are on the same footing, and you can say the weights are the more variable of the two, relative to their size. That is the CV's whole reason for being.

Reading the coefficient of variation

A larger CV means more spread relative to the average, and a smaller one means the values cluster tightly around it. A CV above 1 tells you the standard deviation is actually bigger than the mean. What counts as high or low depends on the field, with tight manufacturing processes wanting a CV well under 0.1 and financial returns often running much higher.

One caution worth keeping in mind: the CV only makes sense for data with a positive mean, like heights, weights, or prices. When the mean sits near zero, dividing by it makes the CV shoot up and become unstable, so it is not a reliable measure for data that straddles zero or can go negative.

A worked example: eight numbers

Take the eight numbers 2, 4, 4, 4, 5, 5, 7, 9. Their mean is 5, and their population standard deviation is 2.

The coefficient of variation is the standard deviation divided by the mean: 2 ÷ 5 = 0.4, which is 40 percent when written as a percentage. So the spread in this set is about four tenths the size of its average.

Entering your data, and the rounding

You can separate your numbers with commas, spaces, or line breaks, in any mix, and the order does not matter. The CV here is built on the population standard deviation and shown as a ratio. If you would rather see it as a percentage and based on the sample standard deviation, our relative standard deviation calculator reports it that way.

Questions people ask

What is the coefficient of variation?

The standard deviation divided by the mean, giving spread as a proportion of the average. Because it has no units, it lets you compare variability across data sets on different scales.

Is the CV a percentage?

It is a ratio, but it is often written as a percentage by multiplying by 100. A CV of 0.4 is the same as 40 percent.

Why use the CV instead of the standard deviation?

The standard deviation is in the units of the data, so it cannot be compared between different kinds of data. The CV strips out the units, making variability comparable across scales.

When does the CV break down?

When the mean is near zero or can go negative. Dividing by a mean close to zero makes the CV blow up, so it is only reliable for data with a solidly positive mean.

References

A quick note on where the methods here come from. The coefficient of variation, as the ratio of the standard deviation to the mean, is set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook covering the coefficient of variation.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of spread). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (measures of the spread of the data). https://openstax.org/details/books/introductory-statistics-2e