Coefficient of Variation Calculator

The coefficient of variation measures spread relative to the mean, so it can be compared across different quantities: it can say whether parcel weights vary more than share prices.

Coefficient of variation

—

Coefficient of variation—

Mean—

Standard deviation—

Reading—

Number of values—

Range—

Measure	Value

How this was worked out

The formula

CV = (s / x̄) × 100

What it means

A standard deviation of five says nothing on its own: it is enormous if the mean is ten and negligible if the mean is ten thousand. The coefficient of variation fixes that by dividing the deviation by the mean, which strips the units away and leaves a percentage. That is what makes it possible to compare the variability of two things measured in completely different ways, which is exactly what standard deviation cannot do.

How to work it out by hand

Work out the mean of the values
Work out the standard deviation
Divide the deviation by the mean
Multiply by a hundred to get a percentage

What is worth knowing

The coefficient is useless when the mean sits near zero, because the division blows up and the result stops meaning anything; and it is invalid outright with negative means or on interval scales such as degrees Celsius, where zero is arbitrary: twenty degrees is not "twice" ten. As a rule of thumb, below fifteen per cent the data are homogeneous and above thirty they are clearly spread out, though those thresholds depend on the field.

Frequently asked questions

Why bother if I already have the deviation?

To compare. Standard deviation cannot be compared across different quantities and the coefficient can, because it has no units.

Does it work with Celsius temperatures?

No. Zero on the Celsius scale is arbitrary and the coefficient assumes zero means absence. With kelvin it would work.

What counts as high?

Above 30 % is usually called high spread and below 15 % homogeneous, but it depends heavily on the field.

What if the mean is zero or negative?

Then it makes no sense to calculate. The division blows up or flips sign, and the resulting number cannot be read.

Does it use the sample or population deviation?

The sample one, which is what applies when the data are a sample. That is the usual case.