The "Average" Scam

A single piece of data or information can have multiple meanings or layers of meaning. This sounds obvious but we do not always instinctively know this. Take, for instance, the notion of “average”; a lot of information or misinformation can be revealed if you scrutinise any “average number” to the required depth.

Let me paraphrase an example given by Nassim Nicholas Taleb in his book “Antifragile: Things That Gain From Disorder”. If you were told that your grandmother would be spending the next 2 hours at a neither-hot-nor-cold average temperature of 23°C. You know that this is an ideal temperature for healthy grandmothers in tropical regions. No worries. 

Two hours later, you are called and told that your grandmother is dead due to a temperature-related shock. As it turns out, she spent the two hours at an “average temperature” of 23°C, but in reality, she spent the first hour at a very cold -10°C and the second hour at a very hot 56°C. So, while 23°C is an accurate numerical representation of the average temperature that your grandmother was exposed to, it is NOT a true representation of the actual experience.

Let us refer to the statistical average as “first-level information”, and the dispersion of the actual data around the statistical average as “second-level information”. While the notion of “average” might be a somewhat reasonable simplification of information, it does not simplify the real-life situation and does not allow you understand the true picture of things, as such, you cannot decide/act/plan accordingly. If you had known that 23°C was an average of widely dispersed data points, you would have made decisions that will keep your grandmother alive (assuming, of course, that you want her alive). 

Consider that you are about to join a company, you have no idea what your actual pay will be but you have been informed that the “average pay” for staff in the department you are joining is N500,000 per month. Coming from a job where you are paid N200,000 per month, is this a good offer for you? It depends. What if an insider informs you that of the 12 staff currently in that department, two of them earn N2.5 million monthly and each of the other ten earns N100,000 monthly which gives the nice average of N500,000 in the department? Does this second-order level information cause you to revise your earlier opinion? Probably.

In both cases, considering just the first-level information, even if you anticipate some variation, your expectation can be depicted as in the figure below, a normal distribution around the mean.

However, when you consider the second-level information, your expectation can be represented similar to the figure below which is much closer to the true physical reality. 

Generally, having a sense for second-, or even third-level information can help you avoid getting scammed by first-level information that can be statistically accurate but, also grossly misleading.