What is the rationale for the normal distribution of intelligence?

I'm asking what the rationale is for saying that 68% of variance within intelligence falls within 1 standard deviation either side of the mean, and 95% within 2, etc.. That's just what "normal distribution" means. Here is a picture:

enter image description here Why not suppose that intelligence is e.g. a uniform distribution? You can see clearly, in the picture below, that if it's modeled in that way:

  • someone's deviation from the mean will be equal to the probability of their score.

enter image description here

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    $\begingroup$ @user3293056 The response so far shows your question is ambiguous. Therefore, I recommend you update your question to clarify what you mean by 'rationale' and that you add a reference where you found the statement "68% of variance falls within 1 standard deviation ...". In addition, in your second paragraph (starting with "To be specific"), it would help to clarify how you understand 'significant'. Lastly, I recommend simply removing the last question. Based on the answers you get, it might become irrelevant or you can then phrase it better (including what you learned). $\endgroup$
    – Steven Jeuris
    Oct 31, 2017 at 13:40
  • $\begingroup$ @StevenJeuris it may help if you name two or more ambiguous ways that you might read the question? $\endgroup$
    – user7852
    Oct 31, 2017 at 16:30
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    $\begingroup$ In regards to 'rationale': "Why is a normal distribution used when talking about IQ results?" (based on prior comments I expect this one to be your question), "Why do IQ results follow a normal distribution?" (what AliceD's answer currently addresses) "What is the rationale behind making IQ results follow a normal distribution?" (what baca's comments seem to refer to). P.s. thank you for the edit! Definitely clarifies your current understanding better. Down vote retracted. $\endgroup$
    – Steven Jeuris
    Oct 31, 2017 at 18:50
  • $\begingroup$ @StevenJeuris well yes i had already pointed to how i was unaware of the central limit theorem. $\endgroup$
    – user7852
    Oct 31, 2017 at 19:11
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    $\begingroup$ You pointed this out in comments to AliceD's answer ... You asked me to point out how the question was ambiguous, I highlighted three different ways in which it could be interpreted. Ideally, you clarify which one of the three specifically you mean. Your question should stand on its own, and not rely on any subsequent comments you make on answers (or even on the question itself). $\endgroup$
    – Steven Jeuris
    Oct 31, 2017 at 19:45

1 Answer 1


Short answer
IQ scores are distributed normally, because they follow the central limit theorem.

When we measure IQ scores in sufficiently large populations, they will be normally distributed. This holds for healthy controls, as well as groups of people with ADHD or reading disabilities (Kaplan et al., 2000), and also in people with mild to moderate mental retardation (Bellugi et al. (2003).

Many biological variables follow a normal distribution quite well. This is a result of the central limit theorem, which says that when you take a large number of random numbers, the means of those numbers are approximately normally distributed (McDonald, 2012). When for example the weight distribution is sampled in a population, it will vary with age, nutrition, disease status etc. The addition of these independent random variables result in the variable (in this case weight) to become normally distributed ("bell shaped"), even if the original variables themselves are not normally distributed (source: wikipedia).

Hence, your statement Do we as a society have the right attitude to variation in human intelligence? Because it seems to me we are either over-nurturing the extremes, or should not represent it as a normal distribution doesn't really apply here, as IQ score distributions have nothing to do with 'us as a society having the right to do something'.

- Bellugi et al., Enfance (2003); 3(55): 237-49
- Kaplan et al., J Learning Disabilities (2000); 33(5): 425-32
- McDonald, Handbook of Biological Statistics, 3rd ed. (2012). Sparky House Publishing, Baltimore, Maryland

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – AliceD
    Oct 31, 2017 at 19:58
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    $\begingroup$ To support what Alice said, we know from GWA studies that the "Heritability [of intelligence ] is caused by many genes of small effect" ncbi.nlm.nih.gov/pmc/articles/PMC4270739 so that's probalby a good enough reason for the central limit theorem to apply to the IQ distribution in a population. The short summary "IQ scores are distributed normally, because they follow the central limit theorem" is too elliptical without mentioning at all why the premisses of the central limit theorem apply to IQ (but I've upvoted nonetheless, because it is explained later, although just by analogy $\endgroup$ Aug 5, 2018 at 10:08
  • $\begingroup$ @AliceD,is IQ test norm measured data or perfect normal distribution data? $\endgroup$
    – kittygirl
    Mar 25, 2019 at 15:39
  • $\begingroup$ @kittygirl normally distributed. No data set will reach perfect normality, at least in this world :) $\endgroup$
    – AliceD
    Mar 25, 2019 at 19:40
  • $\begingroup$ @AliceD,if IQ test norm is not perfect normality,how can we use mean 100 and sd 15 to mesure?Is that means norm of psychology test not completely equal to actual data but artificial normalized? $\endgroup$
    – kittygirl
    Mar 26, 2019 at 1:36

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