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December 10

why don't rankings publish median SAT scores?

the 25% and 75% SAT scores diverge very wildly at most colleges. Why don't they publish median SAT scores? Also, mathematically or in practice (e.g. bell curve) can we arrive at a good estimate of the median given the 25% and 75% scores? (How?) For example by averaging the two? 212.96.61.236 (talk) 01:10, 10 December 2014 (UTC)[reply]

If all we know are the 25% and 75% quartiles, the most reasonable way to estimate the median is by taking either the arithmetic or geometric mean. For symmetric distributions (and I believe SAT scores are symmetric enough for this purpose) the arithmetic mean (simple average) will work very well. For distributions that span many orders of magnitude, such as incomes, the geometric mean might work better. -- Meni Rosenfeld (talk) 17:32, 10 December 2014 (UTC)[reply]

Meni, do we have any guarantee about the error bounds on an arithmetic average? I mean look at something like Harvard which says

"SAT score (25/75 percentile): 2080-2370 "

That is a rather wide range! (690-790). Given that Harvard might fill more than half of its class with people scoring above 2300 (it certainly would have this choice based on applicant pool) we would be quite off in guessing an average based on the 25th percentile. . . Also the 25th percentile could be composed of people who had very strong legacy, and it might simply be limited to 25% of the class by kind of 'quota.' It is hard to say. . . . How much accuracy do you think I should give to a simple arithmetic mean? 212.96.61.236 (talk) 02:12, 11 December 2014 (UTC)[reply]