Coefficient of Variation Calculator — Step-by-Step Solutions

The Coefficient of Variation Calculator measures relative variability by expressing the standard deviation as a percentage of the mean. It is particularly useful for comparing the spread of datasets with different units or scales.

Enter a dataset to calculate the CV directly, provide a known mean and standard deviation, or compare the relative variability of two datasets side by side.

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How to Use the Coefficient of Variation

CV from Dataset: type or paste your values separated by commas. The calculator finds the mean, the standard deviation, the variance and the coefficient of variation as a percentage.
CV from Mean + Std Dev: if you already know the mean and the standard deviation (for example from a published table or from a sample), enter both to get the CV directly.
Compare CVs: enter two datasets to see which one is relatively more variable, even if they are measured on very different scales.
Note that the dataset modes use the population standard deviation (divide by n). If your data are a sample and you want the sample version, work out s separately and use the Mean + Std Dev mode.

Formula and Theory

The coefficient of variation (CV) is the standard deviation divided by the mean, usually written as a percentage. It measures spread relative to the size of the average, so it has no units. A standard deviation of 5 means very different things when the mean is 10 and when it is 1,000, and the CV makes that visible.

Because it is unit-free, the CV lets you compare variability between datasets measured on different scales or in different units, such as the consistency of two machines producing parts of different sizes, or the volatility of two investments with different average returns.

The CV only makes sense for ratio-scale data with a meaningful zero and a positive mean. It is unstable when the mean is close to zero, and it is undefined when the mean is zero. Temperatures in Celsius or Fahrenheit, which have arbitrary zeros, are not suitable.

A low CV indicates consistency; a high CV indicates the values are widely scattered compared with their average. There is no universal threshold, since acceptable variation depends on the field.

Worked Examples

Example 1: CV of a dataset

Problem: Find the coefficient of variation of 10, 12, 23, 23, 16, 23, 21, 16.

Solution: Mean = 144 / 8 = 18. Deviations from the mean: -8, -6, 5, 5, -2, 5, 3, -2, with squares 64, 36, 25, 25, 4, 25, 9, 4, which sum to 192. Population variance = 192 / 8 = 24, so the standard deviation is sqrt(24) = 4.899. CV = 4.899 / 18 x 100 = 27.2%.

Answer: CV = 27.2% (mean 18, SD 4.899)

Example 2: The sample version of the same data

Problem: Treat the same eight values as a sample. What is the CV with the sample standard deviation?

Solution: Sample variance = 192 / (8 - 1) = 27.4286, so s = 5.2372. Enter mean 18 and standard deviation 5.2372 in the Mean + Std Dev mode: CV = 5.2372 / 18 x 100 = 29.1%.

Answer: CV = 29.1%

Example 3: From a mean and standard deviation

Problem: A process has mean 50 and standard deviation 5. What is the CV?

Solution: CV = 5 / 50 x 100 = 10%.

Answer: CV = 10%

Example 4: Which dataset is more variable?

Problem: Dataset 1: 10, 12, 14, 16, 18. Dataset 2: 100, 150, 200, 250, 300. Compare their relative variability.

Solution: Dataset 1: mean 14, population SD = sqrt(8) = 2.828, so CV = 2.828 / 14 x 100 = 20.2%. Dataset 2: mean 200, population SD = sqrt(5000) = 70.71, so CV = 70.71 / 200 x 100 = 35.4%. Dataset 2 has a much bigger standard deviation, and it is also relatively more spread out.

Answer: Dataset 2 is more variable: 35.4% against 20.2%

Frequently Asked Questions

What is a good coefficient of variation?

There is no universal cut-off. Lower means more consistent, and what counts as low depends on the field: a precise instrument is expected to repeat to within a few percent, while the returns on an investment vary far more. Compare against the standard for your own subject.

How is the CV different from standard deviation?

Standard deviation is in the units of the data and depends on scale. The CV divides by the mean, so it is a percentage that can be compared across different scales and units.

Can the coefficient of variation be negative or over 100%?

This calculator uses the absolute value of the mean, so it is never negative. It can exceed 100% when the standard deviation is larger than the mean, which happens in strongly skewed data.

When should I not use the CV?

Avoid it when the mean is near zero or the data can be negative with an arbitrary zero point, such as temperatures in Celsius. The ratio then becomes meaningless or explodes.

Should I use the population or sample standard deviation?

Use the population version if you have every member of the group, and the sample version (divide by n - 1) if the data are a sample. The dataset mode here uses the population version; for a sample enter the mean and your sample standard deviation.

Is the CV the same as relative standard deviation?

Yes. Relative standard deviation (RSD) is another name for the same quantity, often used in chemistry and quality control.