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Coefficient of Variation
What is the Coefficient of Variation?
While the discipline of statistics can help put data into order, dealing with data can be far from orderly. One of the most common types of analysis employed in fields like history, medicine and psychology, is called meta analysis. At its most basic, meta analysis is a review of a diverse range of studies that have been performed in the past for one subject.
The difficult thing about comparing different studies, or even two sets of data, is the fact that you will rarely get data that posses the same characteristics, such as the units measured, mean or sample size. In this case, you may be thinking comparing two or more data sets by way of standard deviation will solve the problem. Standard deviation measures the spread, after all.
However, the standard deviation is really only good at letting us compare values within the same data set. A more accurate way of comparing two or more data sets is to use the coefficient of variation.
The definition of the coefficient of variation is that it is the ratio between the standard deviation and the mean. The formula for the coefficient of variation is different for samples and a population, seen in the table below.
CV for the Population  CV for a Sample 


 The higher the coefficient of variation, the higher the variability of the data set
This means that, when comparing two or more data sets, the one with the highest coefficient of variability can be said to have the highest variation.
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