# What is the coefficient of variation?

The coefficient of variation in terms ofstatistics refers, it is a representation of how is the standard deviation that a sample has with respect to its mean. This concept of coefficient of variation implies the variation that some data can present. This is known as the variability that a variable can present.

## Calculation of the coefficient of variation

To calculate the coefficient of variation, its formula implies the presence of the standard deviation, the result of which can be presented as a percentage. Thus, the mean will also be taken into account in the coefficient of variation formula.

CV = σ/μ

When the coefficient of variation is to be expressed as a percentage, then we will have to do the following, multiply it by 100:

CV = σ/μ x 100

In both formulas CV is the result of the coefficient of variation, also known as relative dispersion in this case. The σ represents the standard deviation and finally the μ is the arithmetic mean in question. In this sense, the greater dispersion will refer to a greater coefficient of variation, that is, a higher percentage.

## In which cases is the coefficient of variation useful?

The applications of the coefficient of variation are useful for all those cases in which you want to compare a set of data, whose dimension is different. Furthermore, the coefficient of variation is applicable when the means are high, that is, even though the total value may be high, the data does not always have to be dispersed among themselves.

It should also be taken into account that a coefficient of variation will be less than one although the probability can vary. That is, to be greater than one. Or conversely, be less than one.

This coefficient allows the calculation of population data and what it does is eliminate the number of dispersions that may occur between the means of the populations that are usually compared.

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