IQ rant

"It is the realisation that by definition half the world has an IQ under 100 and they vote conservative." - From some aimless editorial in the Sydney Morning Herald.

I've heard comments like this so many times, and that was probably the last straw. Wasn't it passed around as a sortof Bushism that George the Shrub was surprised to hear that "half the population was of below average intelligence"? I'm paraphrasing from memory by the way. And two lecturers who really should have known better used that same line in class, as a warning to drive more carefully during the holiday season, because, etc.

Loathe as I am to counter Bush-mockery, he was right to be surprised, because its simply not true that half the population is of below average intelligence. It's doesn't ring true intuitively, and it's not true "by definition" either, because an average of a sample of numbers does not imply that half the sample of numbers lie below the average and so on. People know this, don't they? Am i taking it too seriously? Is it actually a joke that people find funny?

Alright, so IQ is represented in a normal distribution, which is different from a random sample of numbers. Even so, I think there is some confusion in interpreting the curve.

Here is a sketchily drawn (and blurry) representation of the normal distribution of IQ scores in a population.



Perhaps the confusion lies in the understanding of what a normal distribution is, because it is symmetrical across the mean (100), and therefore half of the possible scores lie below 100, and half above it.

However, the population is not distributed that way. As you can see, if you were to be strict about it and decided the average IQ was 100, and 100 only, there is a rather significant number of people that are "average", and hence those groups of people with IQ scores of less than 100 or more than 100 for that matter, cannot reasonably be considered to be half the population.

Moreover, an IQ is not a fixed number, being only a test score, and is usually subject to error of plus or minus 3 points. Not only that, scores within 1 standard deviation of the mean (15 points) are usually considered average, such that approximately 68% of the population has, in fact, an average IQ score, ranging from 85 to 115. Therefore only approximately 16% of the population could reasonably be considered to have a below average IQ score.

In case anyone wants to know, an IQ score of at least 2 standard deviations above the mean is the point at which intellectual giftedness is usually set, although there are variations.

I'll try not to get started on how IQ does not equate intelligence, and go to bed instead. Feel free to ask me any questions, call me a pedant, or argue with me if you don't agree or think I'm taking this too seriously.

:P