Wednesday, December 10, 2008

Statistical Fallacy

Yaknow, maybe it's just me being anal, but there's a common joke/insight/sardonic musing out there that kinda bugs me:

"Remember folks, half of everyone you meet every day is below average".

It gets a quick laugh, and hits that little schadenfreude center in our brains; but it bugs me, because it shows how little most folks know about statistics.

Technically speaking, half the "people you meet every day" are below the median not the average; which is more properly titled the "mean".

Given a gaussian distribution, about 68% of values are within one standard deviation of the mean, about 95% of the values are within two standard deviations, and about 99.7% lie within three standard deviations.

That means, that about 32% of all people are within a statistically insignificant difference from "average" (1/2 a standard deviation or less).

The difference from 1/2 to 1 standard deviation from the mean is generally considered to have a mathematically relevant impact; but in empirical terms generally means very little. It is generally only variations of 1 standard deviation or more which have a significant practical impact.

Thus, only about only about 16% are "below average", to a significant degree (and conversely only 16% are above average to a significant degree).

However, I'd guess that you have to be at least one standard deviation above the median to have understood all that.

Ok, that's just me being a wanker.