Since IQ scores are calculated to conform to a normal distribution, your IQ is in exact correspondence with your percentile ranking in the general population. If f(x) is the CDF of the Normal(100,15) distribution, and your percentile ranking is p, then your “true IQ” is precisely the value of x such that f(x)=p. Since there are only roughly 7 billion people alive, the smartest person on Earth is ranked above 99.99999998578% of other people, which corresponds to an IQ of 195. If we include all people that have ever lived (I believe the number is roughly 100 billion), the smartest would have an IQ of 201.
William Sidis’s IQ of 250-300 is using a different scale, which is no longer used: it claims that his intellectual age, as a child at the time he took the exam (if in fact he did, there is some doubt about this) was 2.5 to 3 times his physical age. This isn’t really a meaningful assessment of how smart he was as an adult, nor does it have any relationship to the modern system of IQ scores (on a normal curve, such a score is 1 in 10^23, which I think we all agree is ridiculous).
Since IQ scores are calculated to conform to a normal distribution, your IQ is in exact correspondence with your percentile ranking in the general population. If f(x) is the CDF of the Normal(100,15) distribution, and your percentile ranking is p, then your “true IQ” is precisely the value of x such that f(x)=p. Since there are only roughly 7 billion people alive, the smartest person on Earth is ranked above 99.99999998578% of other people, which corresponds to an IQ of 195. If we include all people that have ever lived (I believe the number is roughly 100 billion), the smartest would have an IQ of 201.
William Sidis’s IQ of 250-300 is using a different scale, which is no longer used: it claims that his intellectual age, as a child at the time he took the exam (if in fact he did, there is some doubt about this) was 2.5 to 3 times his physical age. This isn’t really a meaningful assessment of how smart he was as an adult, nor does it have any relationship to the modern system of IQ scores (on a normal curve, such a score is 1 in 10^23, which I think we all agree is ridiculous).