The SAT is normally taken by the most academically successful third of U.S. 17-year-olds. The two thirds of American teens who don’t take the SAT have either dropped out of high school long before the SAT is given, or they have no plans to go to a selective college.

However in order to convert SAT scores to IQ equivalents, it helps to know how all American teens would do on the SAT if they took it.

In a series of rare little-known studies, the college board gave a short version of the SAT to a representative sample of all American high school juniors and then statistically adjusted the scores to predict how the would have done at 17 (I think). They could have just waited until they were 17, but by then a lot of them would have dropped out of high school, and thus could not be tested.

Here are the results from 1974 (remember, the SAT got a lot easier in April 1995):

One of the first thing we notice is that the distribution is not perfectly Gaussian at the extremes.  For example a verbal score of 650 is at the 99 percentile which on a normal curve, is 2.33 standard deviations (SD) above the mean (IQ 135; U.S. norms), but according to the actual mean and standard deviation (368 and 111 respectively), it’s 2.54 standard deviations above the mean (IQ 138).  That may sound like a trivial difference but it occurs on the math section too.   The normal curve says a math score of 700 (99 percentile) would be 2.33 standard deviations above the mean (IQ 135) but the actual mean and standard deviation put 700 at +2.66 SD (IQ 140).  These differences add up in the composite score.

I suspect this departure from the normal curve is because some kids attend schools that better prepare them for the SAT than others.

Of course at the very, very high end of the SAT you get the opposite problem.  The normal curve under-predicts how rare scores are.  I suspect this happens because normally on the SAT, if you fail an item that is beneath you, you can recover by solving at item that is above your head.  But when there are no items that are above your head, you can’t compensate for silly mistakes with lucky guesses, making perfect scores especially rare.