<p>I think it’s actually a little bit misleading to consider the statistics as you are: it looks like you’ve drawn the cumulative score range for Columbia from the 2013 profile site, whereas for the other schools you’ve just added up the College Board 25/75 range for each subject; I don’t think the two are equivalent.</p>
<p>To use Harvard as an example: 25% of Harvard students have an 800 in Reading, 25% have a 780 or higher in Math, and 25% have a 790 or higher in Writing, but I’m not convinced that 25% have a cumulative score of 2370 or higher. Put another way: I don’t think the 25% who have an 800 in Reading overlap significantly with the ones who have a 780+ in Math. My reasons are speculative and prejudiced by my experience in which very few people are superbly talented in both the sciences and the humanities, so take it for what it’s worth.</p>
<p>To offer some hard evidence, though, I offer this thread:
<a href=“http://talk.collegeconfidential.com/parents-forum/154634-sat-score-distribution.html[/url]”>http://talk.collegeconfidential.com/parents-forum/154634-sat-score-distribution.html</a></p>
<p>To be clear, the data used in that thread is based on old SAT scores, so if we use Harvard as an example again, we can drop the Writing section score and compare. Based on your aggregation, Harvard’s top 25% of cumulative scores would be, in old SAT terms, a score of 1580+.</p>
<p>One poster relayed the following cumulative score distribution from a 2003 College Board report:</p>
<p>1600 0.07%
1590 0.03%
1580 0.05%
1570 0.05%
1560 0.07%
1550 0.09%
1540 0.10%</p>
<p>Also, there were apparently 1.4 million students who took the test in 2003/2004. Based on the above distribution, this means that 2,100 students had a 1580+. </p>
<p>Harvard’s incoming class is ~1,700, so it’s conceivable that 425 of them had a 1580 or higher, but then there are also Princeton, Yale, Stanford, and MIT among a bevy of similar schools who attract high caliber students. In fact, if you aggregate section scores for Princeton and Yale, their top 25% cumulative range is also 1580+. Theoretically, then, Harvard, Yale, and Princeton alone should attract around 1,100 of the 2,100 students who scored more than a 1580. </p>
<p>It’s certainly plausible - they are great schools with tremendous brand equity and a wide draw. However, there are something like 3,500 institutions of higher education in this country, and while I’m sure that a large number of top SAT scores (as well as SATs taken) are concentrated in the Northeast, it is my understanding that there are entire swaths of the country where there are strong state schools or regionally-reputed privates (i.e. Emory and Vanderbilt in the South, Big Ten schools in the Midwest) that attract top students who don’t even consider Ivies. </p>
<p>This is ultimately a very semantical discussion - the 7.5% RD figure says about all there is to be said for the difficulty of getting into Columbia - but something in me objected, perhaps on statistical principle, to adding 25/75 ranges for each section together and assuming those figures to be representative of cumulative score ranges.</p>
<p>To answer your question, then: I am inclined to think the score range says very little about the admissions process at Columbia, because it’s not at all clear what the score range actually is. I think it’s only intended to be a rough guideline for competitiveness.</p>