Coefficient of Variation Calculator

1. Using the coefficient of variation calculator
2. What is coefficient of variation
3. Formula for coefficient of variation

    Using the coefficient of variation calculator

Here are some brief instructions on how to use this coefficient of variation calculator.

Begin by selecting if you are going to enter summary data: standard deviation and mean / proportion, or if you prefer to enter raw data. If entering raw data you need to choose between continuous data, which you can enter manually or copy/paste from a spreadsheet, and proportions data for which you only need to know the proportion / rate, or the number of events and the total population.

Once these are entered, just press "Calculate" and our calculator will do the rest.

    What is coefficient of variation

The coefficient of variation (abbreviated "CV"), also known as relative standard deviation (RSD) is a term from probability theory and statistics representing a standardized measure of dispersion of a probability or frequency. It is often expressed as a percentage and is widely used in analytical chemistry, engineering and physics, factory production quality assurance. It is also often used in economists and social studies for economic, organizational and financial models.

The CV is a dimensionless number, so it is not dependent on the unit of measurement or the mean of the data.

The major advantages usually cited in favor of using the coefficient of variation instead of the standard deviation are ^[1]:

• it is insensitive to the scale of the measured variable(s), and this scale-invariance makes cross-unit comparisons easier
• it allows to compare differences across groups with significantly different means (relative magnitude of effects)

There are, however, disadvantages to using relative standard deviation instead of the absolute one. For one, it cannot be used to construct confidence intervals for the mean. When the mean is close to zero, the CV approaches infinity, making it very sensitive to small changes in the mean. It is also a poor statistic when the number of observations in the different groups varies, since the CV is invariant to the sample sizes. The standard error of the mean is generally a superior alternative in such cases. The coefficient of variation is often used as a measure for economic inequality, although there is some criticism regarding its utilization in such a manner ¹.

As with any statistic, using a coefficient of variation calculator has its good uses and situations where CV is not the appropriate statistic.

    Formula for coefficient of variation

The coefficient of variation is the ratio between the inverse of the mean and the standard deviation:

CV = σ / μ

where σ is the sample standard deviation and μ is the sample mean. The CV is usually estimated from a sample, but when the population standard deviation is known, it can be used instead. The formula above is used in our calculator essentially assuming the raw data entered is a sample from which the σ is estimated.