Someone who reads my blog sent me this email:
Reading your articles. I am confused between standard deviation and coefficient of variation. Standard deviation itself shows how much variation exists from the average then what does coefficient of variation tells us?
Standard deviation shows the amount of variation. Not related to anything. The variation coefficient shows the relative amount of variation. The standard deviation related to the mean. You should always relate the standard deviation to the mean. Otherwise, you will think height varies a lot among NBA basketball players because they are all tall while height varies little among children because they are all short.
Standard deviation is not a number that ports well. The variation coefficient is. It’s a way of seeing how big the swings above or below the average have been in terms of the average. Have they been one-third of the average? Or have they been the same size as the average?
For example, two companies can both have a standard deviation of 10% in their operating margins over the last 10 years. If one company has an average operating margin of 10% and the other has an average operating margin of 30% – that same 10% swing is going to feel very different. The variation coefficient tells you this. The standard deviation does not.
I need to make two points here. One, I use stats to describe. Not predict. Two, I use stats to compare. To rank. Different people have different reasons for measuring the things they measure.
If your goal – like mine – is to describe the past and compare different company’s pasts to each other, the variation coefficient is the right number to use.