I have a question from my OAC finite class. I've come across a problem with the coefficient of variation. I have taught my students that there are no units for coefficient of variation and it can be expressed as a percent. So, for example, a set of data with mean of 5 and standard deviation of 100 would have a CV of 5%. But what happens in this situation: the mean is 4meters and the standard deviation is 0.7mm. Is the CV 1.75% or 0.00175% or 0.0175%? I've had some students change leave the units as is, change them both to mm or change them both to meters...so which is it and why?
The coefficient of variation as a percent is
You are quite right that the coefficient of variation is unit free, but only if the mean and standard deviation are measured in the same units. With a mean of 4 meters and a standard deviation of 0.7 millimeters you should convert the units of one of the quantities so that both are in the same units.
To express both quantities in millimeters, 4 meters is 4 x 1000 = 4 000 millimeters and thus the coefficient of variation is
You could also express both quantities in meters. In this case 0.7 millimeters is 0.7/1000 = 0.0007 meters and the coefficient of variation is