# Coefficient of Variation - Explained

What is the Coefficient of Variation?

# What is the Coefficient of Variation?

According to probability theory and statistics, the standardized measure of the dispersion of a probability distribution or frequency distribution is referred to as the coefficient of variation (CV). It can also be called "Relative Standard Deviation (RSD). Its value is usually expressed in percentage. In simple terms, the coefficient of variation (CV) is simply the ratio of the standard deviation to the mean. The greater the coefficient of variation, the greater the dispersion level around the mean. The coefficient of variation is usually computed for only sets of data which are measured on a ratio scale. This means it should be used for scales having a meaningful zero. The coefficient of variation can be mathematically expressed as: Coefficient of Variation = Standard Deviation / Mean The standard deviation is defined as a measure of the amount of variation or dispersion of a set of data. A low standard deviation reflects that the data tend to be close to the mean of the data set. A high standard deviation on the other hand, reflects that the data is spread out over a wider range. The mean of a data set also called the average, is the central value of a discrete set of numbers. It can be derived by summing up the values of the data set and dividing them by the number of values present in the data set.

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## How is the Coefficient of Variation Used?

The coefficient of variation is especially useful when comparing results from two different surveys or analyses that have different measures or values. It is usually computed for only sets of data which are measured on a ratio scale. When values to be computed are without units, the CV helps to compare the distributions of values whose scales of measurement are not comparable. When estimated values are to be computed, the CV relates the standard deviation of the estimate to the value of this estimate. The lower the value of the coefficient of variation, the higher the precision of the estimate. The coefficient of variation may not have any meaning for data on an interval scale.

## Example of Coefficient of Variation for Selecting Investments

Looking at an example of a researcher who is trying to compare two samples A and B with different conditions. The results from the two samples are: Sample A Sample B Mean 59.9 44.8 SD 10.2 12.7 Calculating the CV using the formula CV = (Standard Deviation / Mean)*100 gives the data below: Sample A Sample B Mean 59.9 44.8 SD 10.2 12.7 CV 17.03 28.35 Looking at the standard deviations of A and B, the researcher might think that the samples have similar results. However, when he adjusts for the difference in the means, the results have more significance: CV of A = 17.03 CV of B = 28.35

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