Coefficient of Variation

The Coefficient of Variation (CV in short) is simply the standard deviation relative to the mean. It's calculated by dividing the standard deviation by the mean.

CV = σ / μ

That's a simple calculation, but why do we need yet another measure when the standard deviation is already doing a good job of measuring variation?

Say you want to compare two data sets. Using the standard deviation to do that would be meaningless as it is an internal measure (as in it is measuring the variation within the data set) and can't be used to compare with another.

This is where you use CV as it elevates, so to say, the standard deviation to becoming a comparable figure.

Here's an example to help you see the point with clarity.

Back to our pens example. Let's say you produced two varieties of pens in the same plant and want to compare the processes. One of the two pen varieties has a standard deviation of 0.25 mm for the diameter, whereas the other has a standard deviation of 0.3 mm for its diameter. Instead of jumping the gun and calling the process for the second pen variety less controlled, you could consider their means as well. The means for the two processes happen to be 7 mm and 9.5 mm, respectively.

Let's calculate the CV for these two.

In the case of the first pen variety, the CV comes to 0.25 / 7 = 0.0357

In the latter's case, it turns out to be 0.3 / 9.5 = 0.0315

Turns out the second pen variety has a more controlled production process.

The bottom line, use CV instead of standard deviation when comparing two data sets for variation.