I thought about this while reading some threads.
SAT ranges can potentially be very misleading. They are, of course, the 25th and 75th percentiles of first year students. They are not the 25th and 75th percentiles of those accepted.
Take School A for an example (average school that is fairly selective and somewhat prestigious).
Of the SAT range of those accepted (not of first year students), those with lower scores are more likely to go to School A rather than those with higher scores (who will be more likely to get into a more prestigious school and choose to go there).
This therefore means that the SAT ranges of admits at fairly prestigious schools are likely to be higher than those shown (which could potentially be bad news). It would only mean, though, that if your score is above the range, you may actually be near the middle of those accepted. So don’t count on your score too much. (This is also where schools like Tufts like to reject students who have scores that are too high, because the student may be using Tufts as a safety.)
There is not, of course, a very strong relationship, but would this make sense? Anyone know?