The fallacy of averages

A discussion with a portfolio company CFO yesterday reminded me that statistics are a dangerous thing and averages are misleading.

‚ÄúThere are three types of lies — lies, damn lies, and statistics.”

Skewed distribution

Most businesses analyze their performance using overly simplistic tools. For an extreme example, imagine a scenario where the average customer produces monthly recurring revenue of $10,000. Well, it is one thing if the MRR of each of the individual customers is scattered tightly in a normal type of distribution around the $10k MRR level. It is another thing entirely if the distribution is skewed like in the image here. For example, what if a small handful of customers are significantly larger than all of the others and are skewing the mean (or average) upward. In such a scenario it is possible that the company is losing money on every one of the smaller customers and making a boatload of money on the larger ones. Unfortunately, there would be many more small customers than large ones (ie the median is lower/smaller than the mean).

If management’s understanding of the business is limited to the average, they might be inclined to pursue a strategy of getting more customers regardless of customer size and profitability, which could result in the company recruiting many more small, unprofitable customers. Rather than looking exclusively at averages, I suggest it is important to look at the distribution in the form of a histogram. More often than not, looking at the histogram leads to conclusions that are obfuscated by the average.

Don’t make decisions based on averages unless you know the distribution around the average is normal. If you suspect the distribution is skewed, put a histogram together and make decisions based on the histogram.

The fallacy of averages