IQ of 160 is a 1 in 100,000. 165 is probably 1 in 500,000. The odds of any one person posting at AT being that high is very low, even if you assume that AT posters are on average high-average. There are lots of claims made of extraordinarily high IQ's (i.e. over 150) by people on the internet and elsewhere. Some may be basing it on a single testing that is actually an outlier, or on a single test that is poorly constructed. Still others are engaging in puffery. Still others may be telling the truth. There is no way to tell in an individual case.
- wolf
Um, no.
Assuming a standard deviation of 15 points, approximately 1 in 30,000 data points is 4+ sigma above the mean on a Gaussian distribution. So, in theory, 1/30,000 people have IQs of 160 or more.
However, the IQ distribution doesn't form a perfect Gaussian: In fact, there are more extremely high (and extremely low) IQs in the male population than would be expected for a Gaussian (the so-called "high end skew"). So the actual incidence of 160+ IQs is somewhat higher (perhaps 1/20,000).
If the standard deviation is 16 points (which is true of several IQ scales), an IQ of 160 is only 3.75 sigma, with a Gaussian probability of about 1/11,000 (and, again, an even higher incidence in practice).
A 165 IQ (= 4.33 sigma) has a Gaussian probability of approximately 1/50,000.
I've computed the above values using the Taylor expansion (to 30 terms) for the cumulative distribution function for the Gaussian.
Edit: Oops. Turns out I needed more terms for the 165 case: I re-ran everything with 50 terms, and get Gaussian odds of approximately:
3.75 (160 on 16-point scale) sigma: 1/11,000
4.0 sigma (160 on 15-point scale): 1/32,000
4.333333333 sigma: 1/134,000
The values change very little with even more terms.