KNOWLEDGEBASE - ARTICLE #1088

What is the coefficient of variation?

The coefficient of variation (abbreviated CV) is a way to quantify scatter. It is defined as the standard deviation of a group of values divided by their mean. Often that ratio is multiplied by 100 to express the coefficient of variation as a percent (abbreviated %CV).

It only makes sense to compute a CV for ratio variables. This means the variable must have  a true zero. So it is ok to compute a CV for variables such as weight, time, distance, enzyme activity... But it is not ok to compute the CV for variab3es such as temperature (in C or F) or pH. For these variables, the zero point is arbitrary. A temperature of 0 in C or F does not mean 'no temperature'. A pH of 0.0 does not mean 'no pH'.  WIth these variables, you could sensibly choose to define zero differently. If you did, you'd get a different CV, which makes the CV no longer a sensible way to quantify variation.

The CV is useful for comparing scatter of variables measured in different units. You could ask, for example, whether the variation in pulse rate is greater or less than the variation in the concentration of serum sodium.  The pulse rate and sodium are measured in completely different units, so comparing their standard deviation would be nonsense. Comparing their coefficients of variation might prove useful to some physiological investigations of homeostasis.
 

Prism 5 computes the CV as part of the column statistics analysis.

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