A recent paper, "Does Affirmative Action Lead to Mismatch: A New Test and Evidence" by four economists (Arcidiacomo, Aucejo, Fang, and Spenner) has some inside info from the Duke U. admissions department on Duke students, including SAT scores and freshmen grades. The table on p. 14 shows the standard rank order — Asian, white, Latino, black — on most of the various measures that the Admissions department worries about, as well as freshman grades. The overall results aren't surprising:
An SAT gap between whites and blacks of 136 points is not particularly large. (The Bell Curve lists SAT gaps from the early 1990s for 26 well-known colleges, ranging from 95 points at Harvard, the apex predator in the black recruitment game, to 271 at Rice, which is a small school that competes in big time sports, so a high proportion of Rice's black students are also jocks.) Perhaps Duke's famous basketball team raises its profile in the black community, letting it do well in recruiting strong black students (e.g., its black basketball players tend to be from upscale backgrounds, like Grant Hill and Shane Battier, plus Italian-speaking Kobe Bryant and his 1100 SAT score were headed to Duke from Lower Merion Prep until the Lakers picked him straight out of high school).
The standard deviation for white students on the SAT (100) is about half of what it is for whites overall, so the 136 point racial gap is equal to 1.36 standard deviations. In contrast, the GPA gap is only about 0.94 standard deviations, probably due to to blacks taking easier courses.
The economists are concerned about investigating whether or not affirmative action admissions to Duke could hurt the NAM students by tossing them in over their heads. To my mind, it all depends on something they don't look at: intended major. If you just want a soft major, then you should of course take any opportunity presented to you to attend an elite private college with a huge endowment. High tuition colleges don't flunk out many people, so about the worst that could happen to you is that you spend four years feeling like Michelle Obama or Sonia Sotomayor, worried that people can tell that you got in on affirmative action and angry at them for noticing. But, really, cry me a river ...
On the other hand, if you want to major in something hard like mechanical engineering, then maybe you shouldn't jump in too far over your head.