# Why does IQ have a truncated normal distribution?

I know that the IQ statistic is designed to give it a mean of 100 and that you'll certainly never find someone with an IQ below 1 or above 300, but that tells us very little about the variance or general shape of the distribution. So why is it that every graph of IQ scores that I've seen appears to be a truncated normal distribution? Is it some property of the test design, some property of the test subjects, or some deep theorem in statistics that I've overlooked?

• Can you provide examples?
– user17122
Mar 28, 2020 at 22:27
• @baca Every Google Images result for "IQ graph" that I've ever seen. Mar 29, 2020 at 1:26
• I don't understand. The first pictures for me when I go to google "IQ curves" are these ones: iqtestforfree.net/images/iq_bell_curve.gif iqcomparisonsite.com/Images/NormalCurveSmall.gif external-preview.redd.it/… Those are perfectly normal curves (pun intended).
– user17122
Mar 29, 2020 at 4:12
• @baca They're obviously not a normal normal distribution. Nobody has a negative IQ score and nobody has an IQ over 10,000. My question is why they're normal distributions in the first place. Why they're truncated is obvious. Mar 29, 2020 at 14:20
• Although not a duplicate, the answer to this question probably also answers yours. Mar 30, 2020 at 16:49