I just looked at the table that I linked to before:
http://www.iqcomparisonsite.com/iqtable.aspx
I now realize that I was giving the probability of a 172 I.Q. from the Stanford-Binet part of the chart (which is based on a standard deviation of 16 points), rather than the Wechsler part of the chart (which is based on a standard deviation of 15 points). On the Wechsler chart, an I.Q. of 172 only happens once in 1,258,887 people. So in a U.S. population of 129,824,939, we can only expect to see 104 people with an I.Q. of 172 or greater if the Wechsler score is used.
Most people don’t understand how a measure based on standard deviations works. They think that small changes in the numbers don’t make much of a difference, when they actually do. So if you are told that someone has an I.Q. of 140 (on the Wechsler scale), that’s what one person in 261 has, which means that someone in your high school graduating class if you went to a large high school (or in your entire high school if you went to a small one) probably has at least that I.Q. So you’d think that an I.Q. of 150 is only a little smarter. But only one person in 2,330 has that I.Q. or greater, so in your town or neighborhood of that size there might be one person with that I.Q. An I.Q. of 160 is even rarer, since only one person in 31,560 has that I.Q., which means that you’d have to search an entire small city to find a person with that I.Q., and it means that you may well never have talked with anyone with that I.Q. An I.Q. of 170 only happens once in 652,598 times, which means that you’d have to search most of a big city (or a small state) to find someone with that I.Q., and you’ve probably never talked with someone with that I.Q. An I.Q. of 180 only happens once in 10,016,587 times, so there are only about 31 people in the U.S. with that I.Q. An I.Q. of 190 is ridiculously improbable. Only one person in 1,009,976,678 has it, so there are only 7 people in the world with that I.Q. An I.Q. of 200 is even more ridiculously improbable, since only one person in 76,017,176,740 has that I.Q., which means that only about one or two people in the entire history of humanity was at that level, since the usual estimate of the number of people who have ever lived is about 100 billion.
I would use the following rule of thumb: If someone claims to have an I.Q. greater than 160, they’re probably lying. The normal I.Q. tests can’t measure higher than that. There are special tests that claim to measure higher I.Q.'s, but they are not generally acceptable as reliable. It’s also possible that a claim of a higher I.Q. comes from the older tests which use the quotient definition rather than the standard deviation definition, but that could only be if someone was tested at least fifty years ago and is still quoting their score from that test.