quote from another thread:
This is based on the following:
100 is the midpoint, the mode and the median. About 68,26% of the population always score in the range from 100+15 and 100-15, which translates into an average IQ of 85 to 115.
By the way, of course 34,13% scores between 85 and 100, as well as 34,13% of the population scores between 100 and 115. And because of that, the whole range in considered as 'average'.
If we said an IQ between 80 and 100 is average, then it's not correct according to Gauß.
About Mensa...
I don't know about Mensa elsewhere, but it seems highly unlikely that there's an official statement on IQs, because depending on the test, an IQ score of 118 is equivalent to that of 130 which means highly gifted and Mensa level.
So it should say only the top 2& are allowed in (as Mensa International still says), because it's useless to talk about IQ numbers when talking, when percentile ratings matter in comparisons.
It's one thing to have an IQ of 172 in American tests or tests that use a sd of 24. Someone who has an IQ of 146 in a tests that is based on a sd of 15 is still brighter, if only just. (172 = 145)
Officially it's rather impossible to score higher than 145 though. Everything that goes higher than the third sd is guesswork. And guesswork tends to be tricky. It can be accurate, but there's no indication that it is so.