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Coefficient of Variation Calculator

Enter your data, select sample or population, and click 'Calculate' to determine the coefficient of variation step-by-step

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Coefficient of Variation Calculator

Use this coefficient of variation (CV) calculator to determine the standard deviation relative to the mean for a sample or population. By calculating the mean, standard deviation, and CV, our calculator provides insights into the data’s dispersion, making it easy to compare variability across different datasets.

What Is The Coefficient of Variation (CV)?

The coefficient of variation is a statistical measure that expresses the relative dispersion of data points in a dataset. It is calculated as the ratio of the standard deviation to the mean. CV is also referred to as the root mean square deviation (RMSD).

In simple terms, CV measures the relative variability around the mean. It is especially useful when comparing datasets with different units or scales. A higher CV indicates greater variability, which may imply higher risk in financial or experimental contexts.

Coefficient of Variation Formula:

For a Sample:

CV = s x̄

Where:

s is the sample standard deviation
x̄ is the sample mean

For a Population:

CV = σ μ

Where:

σ is the population standard deviation
μ is the population mean
CV represents the coefficient of variation

How To Calculate The Coefficient of Variation?

Example: Calculating the Coefficient of Variation

Find the CV for the sample values: 45, 50, 55, 60, 65.

Solution:

Step #1: Calculate the Mean

Mean = (45 + 50 + 55 + 60 + 65) 5

Mean = 55

Step #2: Calculate the Standard Deviation

SD = (1 / (5 - 1)) * [(45 - 55)² + (50 - 55)² + (55 - 55)² + (60 - 55)² + (65 - 55)²]

= 62.5 / 4

SD = 5

Step #3: Calculate the Coefficient of Variation (CV)

CV = 5 55

CV = 0.0909 (approximately 9.09%)

This example shows how the CV allows you to compare variability relative to the mean. For larger datasets or multiple comparisons, our CV calculator provides quick and accurate results.

References:

Wikipedia: Coefficient of Variation (CV).
Sørensen, J. B. 2002. The Use and Misuse of the Coefficient of Variation in Organizational Demography Research.

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