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What you are missing is the fact that the colleges have the power to manipulate the statistics, and they have a particular incentive to do so with regard to SAT scores because of the impact of those scores on US News rankings.</p>
<p>I would strongly suggest that you read the book The Gatekeepers to get a sense of how highly selective colleges look at test scores and work to manipulate the numbers during the admission process. In the college profiled in the book (Wesleyan), the adcom received frequent updates as to how their SAT numbers were running. They had a target, which was to keep the score range equal or above the previous year's. They did NOT simply solve that problem by opting for high scorers all the time -- rather, all of the ad reps had some favorites among low scorers that they wanted to pitch for admission, and the status of the running average was a factor which governed whether the student could be admitted. If the numbers were high -- then there would be room for some leniency in score range -- whereas if the numbers were running low, they would need to opt for some more high scorers.</p>
<p>Also, keep in mind they are working primarily with medians, not averages - which means that they don't have to do a an exact numeric counterbalance. If they are taking in 1000 students and want to have 75% of the students in with scores above 700.... then they need 750 students who have scores above 700. The other 250 can have any scores whatsoever -- theoretically it doesn't make much difference whether it is score of 650 or 500 -- although of course the ad coms are going to use some common sense and not accept a student whose scores are so low that they can't do the work.</p>
<p>It gets more complicated, because the colleges report the test scores separately, now with 3 separate tests. They do not need across-the-board 700+ scorers -- as long as within each category they have the requisite 750 students. So a 620 Math, 730 CR kid essentially can be counter-balanced with an 800 Math, 600 CR kid -- as long as there aren't too many of them. </p>
<p>So -- going back to The Gatekeepers, I wouldn't be suprised if on some Monday morning the admissions director gets a report from the number cruncher telling him that the school is running great on the CR scores... but is slipping on the math -- so word goes out to the rest to the committee to grab more kids with high math scores. So maybe that's the week some kid with weak EC's but really great math scores gets lucky, and gets in despite lack of any special hook. </p>
<p>I suspect that the total number of admitted kids with at least one score below the 25th mark would probably be more like 30-35% (and those with across the board low scores much more rare). If there were no overlap among low scorers, it would be theoretically possible to have 50% of the students be below the 25th percent mark on one score or the other.... but I think that is unlikely. However, I do think it is more likely that a student with only below-25% score would be admitted than a student with 2 below 25% scores - for obvious reasons.</p>