Minimum and Maximum IQ

So apparently IQ is a way of assigning a number to your performance on any test of intelligence, based on a normal distribution of test takers where the number 100 is assigned to the mean score with 15 taken as the standard deviation. If this is the case, then what is the minimum (maximum) IQ? Well that would be when you score worse (better) than all 8 billion people on the planet.

Well there you have it, the highest possible IQ must be 192.89 and the lowest possible IQ must be 7.11. Seven eleven, it must be true, QED.

The holy Guiness Book however tells us that somebody had an IQ of 238. That’s more than 9 standard deviations away from the mean!!! What does that mean?

This means that in order to have that 238 IQ you have to be better than a population of 6.37 * 10^16. That’s a lot of persons!


Perhaps you are thinking that these tests don’t really have a normal distribution, perhaps the tail is thicker on the right for these pattern recognition or Stanford-Binet tests, making the above calculations somewhat invalid. Well yeah, maybe so. But then why would we be using this IQ normal distribution number to rate them? Pick another rating system. Chess players and downhill racers seem to have some pretty good systems for assigning a number to combatants ability to win, surely the Stanford-Binet sponsors could do something similar?

For a final exercise, lets calculate how many people need to beat you on an IQ test for your IQ to be negative fifty. I’ll let you plug the numbers into the calculator this time. I get something around 10^20, right around the number of possible rubix cube scrambles. QED!


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