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Regarding your first footnote, IQ is assumed to be a normal distribution since that is how it is defined: Measure a factor g of general intelligence, then trans

Regarding your first footnote, IQ is assumed to be a normal distribution since that is how it is defined: Measure a factor g of general intelligence, then translate its distribution of values onto a Gaussian distribution with a mean of 100 and standard deviation of 15. Since IQ is a relative measurement against the population, it can be distributed however one likes. That's not to say, though, that absolute intelligence (however one chooses to define it) is necessarily normally distributed.

dhosek 5y ago
I guess my biggest question is whether the distribution is symmetrical. I think mathematically¹, that if you do something like sum n values that are uniformly distributed from 1…k, you'll tend towards a bell curve as n ∞, so I have no reason to believe that you wouldn't get something like that with IQ tests, but I have a hard time convincing myself that it's necessarily so. Then again, whatever deviation from a pure normal distribution would probably not be dramatic and the median = 100 line would hold up regardless thanks to the definition of 100. --- 1. I've taught basic stats in the past, but my own stats education is rudimentary since I avoided anything that even vaguely approached applied mathematics in my mathematical education.
- barrkel 5y ago
  Intelligence distribution may not be symmetrical. I don't think it is, in fact I'm not sure what that would even mean. High intelligence means doing some things faster and low intelligence means not being able to do some things at all. The only way to symmetry or otherwise is via a quantification which converts these things to a scalar measure, and then distribution becomes a tweakable property of the quantification when tested against a population. And that's why IQ (not intelligence, they are not synonyms) is normally distributed. It is a tuned quantification, designed to be normally distributed. If it doesn't turn out that way, there is some divergence between the population it was tuned for and the sample you're measuring.

dhosek 5y ago

I guess my biggest question is whether the distribution is symmetrical. I think mathematically¹, that if you do something like sum n values that are uniformly distributed from 1…k, you'll tend towards a bell curve as n ∞, so I have no reason to believe that you wouldn't get something like that with IQ tests, but I have a hard time convincing myself that it's necessarily so. Then again, whatever deviation from a pure normal distribution would probably not be dramatic and the median = 100 line would hold up regardless thanks to the definition of 100. --- 1. I've taught basic stats in the past, but my own stats education is rudimentary since I avoided anything that even vaguely approached applied mathematics in my mathematical education.

barrkel 5y ago
Intelligence distribution may not be symmetrical. I don't think it is, in fact I'm not sure what that would even mean. High intelligence means doing some things faster and low intelligence means not being able to do some things at all. The only way to symmetry or otherwise is via a quantification which converts these things to a scalar measure, and then distribution becomes a tweakable property of the quantification when tested against a population. And that's why IQ (not intelligence, they are not synonyms) is normally distributed. It is a tuned quantification, designed to be normally distributed. If it doesn't turn out that way, there is some divergence between the population it was tuned for and the sample you're measuring.