The variance and standard deviation informs us about the variation of one variable. To determine which variable has a higher variability it would not be fair to simply look at the standard deviation. If one teacher decides to mark on a scale of 0 to 10 and obtains a standard deviation of his grades to be 2.3, while another teacher who marks her exams on a scale of 0 to 100 and obtains a standard deviation of 21.8. It is clear that 21.8 is bigger than 2.3 but this does not mean that the students score more varied. The scale used has an impact on the standard deviation itself.
To compensate for this Pearson (1896) introduces the term coefficient of variation, and simply divides the standard deviation by the mean. It is then often multiplied by 100 to obtain a percentage. If the mean is 64 and the standard deviation 21.8, then the coefficient of variation (V) is equal to 21.8 / 64 ≈ 0.34, or 34%.
References
Pearson, K. (1896). Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity, and Panmixia. Philosophical Transactions of the Royal Society of London. (A.), 1896, 253–318.
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