<p>Boarding schools can’t actively go after middle-class students because of the numbers involved. There must be a mindboggling number of very bright, motivated, undereducated kids in this country, many of whom would jump at the chance to go to boarding school if they knew about it and saw it as a possibility. Imagine the competition if the word got out! 
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<p>It’s much simpler, and of course quite laudable, to try to identify some very bright, very disadvantaged students and give them a boost (although I don’t think eligibility for such programs should be determined only by ethnicity). However, this leaves less FA money for kids outside such programs, who are not identified by or eligible for them, i. e., the bulk of the population. Of course, the bulk of the population does not try to send children to boarding school. Still, I do wonder what the applicant distribution by income looks like and likewise what the admission rate is by income (information we are not likely to ever find out). My guess is that the middle-class students who learn about and apply to selective boarding schools are an exceptionally bright and motivated group who ought, in a fairer world, to have a high admission rate but who in fact have a comparatively low admission rate.</p>