IQ scores are supposedly put on a normal distribution with a standard deviation of 15.
The population of the world is about 7,674,000,000.
So, if I know my statistics and made no numerical errors, the smartest person in the world (even given the unrealistic assumption that we could measure everybody's intelligence), would only have an IQ of 194.8083.
Double the population of the world and the max measurable IQ only goes to 196.4.
Given this, why do I see occasional reports of measured IQs above 200? A 200 IQ, statistically, would require a population of at least 76 billion people, ten times more than there are humans now. A 220 IQ would require 10,000 times as many people as that.
Does the math and statistics just get ignored for those high scores, or is the scale different somehow?