The SAT is taken only by students applying to college, who are on average smarter than high school juniors and seniors in general.... I saw a study once showing that the average SAT score on an unselected sample of high school seniors was considerably lower (maybe 100 points for math + verbal) than the average of students who sign up to take the test.
You'll have to show me that study before I can comment on it. How old is it? How many students were in the sample? Did they only test students who did NOT sign up for the SAT as part of the unselected sample? Etc.
On page 422 of The Bell Curve there is a table of SAT scores (actually derived from the PSAT) from national norm studies conducted by the ETS in various years. "The results are summarized in the table below, adjusted so as to represent the mean score that all American juniors would have received on the SAT had they stayed in school for their senior years and had they taken the SAT."
year verbal_mean math_mean
1955 348 417
1960 374 410
1966 383 395
1974 368 402
1983 376 411
The SAT has been normed to have average verbal and math scores of test-takers equal to 500, so at least through 1983 there was a large difference between the average SAT-taker and the general high school population. As the proportion of students taking the SAT has increased, this difference has shrunk, but I think it is still significant.
Here is some more recent evidence along the same lines.
Mean SAT scores by state along with participation rates are shown at
http://www.commonwealthfoundation.org/policyblog/detail/sat-scores-by-state-2011 . Maine has the lowest average SAT score of 1391 for the three sections combined, because it uses the SAT as the high school NCLB test and therefore has a participation rate of 93%. On the NAEP, Maine is about average.
