How to use the coefficient of variation calculator
- Choose Mean and SD if you already have both numbers, or List of values to paste your data and let the tool compute them.
- For a list, choose whether the standard deviation should be the sample version (divide by n - 1) or the population version (divide by n). Use the sample version if your data are a sample of something larger.
- Read the coefficient of variation as a percent. It is the standard deviation expressed as a share of the mean.
- Compare the result across data sets that are in different units or on very different scales.
Formula
Coefficient of variation = standard deviation / |mean| x 100%
Sample SD = sqrt( sum of (x - mean)^2 / (n - 1) )
Population SD = sqrt( sum of (x - mean)^2 / n )
The result is a pure percent with no units, which is why it can compare data measured in dollars, pounds or seconds.
Two production lines
A line fills bags with a mean weight of 50 grams and a standard deviation of 5 grams. The coefficient of variation is 5 / 50 = 0.10, or 10%. A second line fills larger bags with a mean of 500 grams and a standard deviation of 25 grams, which is 25 / 500 = 5%. The second line has the larger absolute spread but the smaller relative spread.
For the list 12, 15, 15, 18, 21, 22, 22, 30 the mean is 19.375 and the sample standard deviation is 5.6553, so the coefficient of variation is 29.19%. With the population standard deviation of 5.2900 it would be 27.30%.
When the coefficient of variation helps
A standard deviation of 5 means something very different when the mean is 10 than when it is 1,000. Dividing by the mean puts the spread in proportion, so you can ask which process, product or investment is more variable relative to its size. It is common in lab work, manufacturing and finance for exactly this comparison.
It works best for data on a ratio scale, where zero means none of the thing and all values are positive, such as weights, prices or durations.
Cases where it misleads
The measure blows up when the mean is close to zero, because you divide by a tiny number. It is also not meaningful for scales with an arbitrary zero, such as temperature in degrees Celsius, where shifting the zero changes the mean but not the spread.
If you want the underlying spread figures first, use the standard deviation calculator or the descriptive statistics calculator, then bring the mean and standard deviation back here.
Assumptions and limits
- The standard deviation and the mean come from the same data and the same units.
- For a list, the sample standard deviation divides by n - 1 and the population standard deviation divides by n. The tool shows which one it used.
- If the mean is negative the tool divides by its absolute value and warns you.
- A mean of exactly zero is rejected, because the ratio is not defined.
Frequently asked questions
How do you calculate the coefficient of variation?
Divide the standard deviation by the absolute value of the mean and multiply by 100 to get a percent. A mean of 50 and a standard deviation of 5 give 10 percent.
What does a high coefficient of variation mean?
It means the values are widely spread compared with their average. Whether that is a problem depends on the field, so compare it with your own earlier data or with another data set rather than with a fixed cutoff.
Should I use the sample or the population standard deviation?
Use the sample version when your numbers are a sample drawn from a larger group, and the population version when you have every member of the group. The sample version is a little larger, so the coefficient of variation is a little larger too.
Can the coefficient of variation be negative or above 100 percent?
It cannot be negative here because the tool divides by the absolute value of the mean. It can exceed 100 percent when the standard deviation is bigger than the mean, which happens with very skewed data.