this post was submitted on 07 Jul 2023
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This is actually possible. Not yet though. IQ only measures how smart you are compared to other people. If everyone took the same IQ test and there would be around 13 billion people then there would be like one or two people with negative IQ. The bell curve onto which you are sorted is never zero, so you just need so many people n that the integral from negative infinity to 0 is at least 1/n.
Isn't there a hard floor though? IQ would have been such a bummer if they set the average at zero ๐คฃ
No, funnily there is no limit. It is just a standard normal distribution with a mean of 100 and standard deviation of 15. You can read more on wikipedia's 'intelligence quotient' under the section 'current tests' where you could click on the links to learn more about the mathematics. Setting the mean to 100 rather than zero was probably so people wouldn't get offended as easily ๐
Negative IQ would be more than six sigmas away. I don't think the distribution would hold till tail that far ๐ค
I was wring abou the 13 billion. It's more like 76 billion. But you can reach any number with enough tests.
https://www.wolframalpha.com/input?i=1%2F%28Integrate%5B1%2F%2815*Sqrt%5B2%CF%80%5D%29e%5E%28-0.5%28%28x-100%29%2F15%29%5E2%29%2C%7Bx%2C-%E2%88%9E%2C0%7D%5D%29
I'm not talking about the normal distribution being valid at some value. Since it's a continuous decaying function in either direction, it'll be kosher at any real number. I'm talking about the hypothesis that IQ will be normally distributed not holding at that far deviations.