Monday, 15 April 2013


In discussions on the internet, when discussing groups of people, quite often these people are divided into two groups: The haves and the have-nots, the good and the bad, the intelligent and the stupid, the hardcore and the casual, and so on. Statements about these two groups are usually made as if there was a clear distinction between them. In mathematical terms, if you plotted something like video game skill on the x-axis and the number of people having this skill on the y-axis, people talk of it as if the distribution was bi-modal; that is as if the curve would have two distinctive humps, one of good players and one of bad players.

Scientifically speaking that is utter nonsense. The Central Limit Theorem says that if you make for example this plot of video game skill of a large enough population, what you will get is a bell curve with a single hump in the middle. That is why this curve is called a "normal distribution". The nature of this curve is that 68% of people are within one standard deviation of the average.

For example 68% of people have an IQ between 85 and 115, and are thus of average intelligence. Of course people are notoriously bad at estimating their own IQ or other qualities, so that if you rely on self-assessment you end up with the observation that most people are above average, which is a mathematical impossibility.

No comments:

Post a Comment