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Source citing any or all of above properties?

Wow! You really need sources to prove to yourself that MIT students are smarter on average than a typical first-year student chosen at random from any University or Community College in the US?

Not in my experience. I've met numerous MIT grads, and invariably they're smarter than the average grad from a less demanding school. Obviously that also applies to Caltech, Chicago, most Ivies, etc. But part of that equation is that the MIT alum learned not only how to survive that greater workload, but they learned more because of it. So they have a head start on several counts.

http://www.prepscholar.com/sat/s/colleges/MIT-SAT-scores-GPA

(First google result, I didn’t verify further)

It is admittedly only a proxy, but the entrance SAT math scores for MIT students are 770 for the 25th percentile and 800 at the 75th percentile.

Put another way: the test that is a helpful differentiator of intellectual ability of the general college population is not a good differentiator for the MIT population because a large proportion max out the scale.

Raven's progressive matrices and similar are differentiator of intellectual ability. SAT scores correspond to time spent on chair doing homework.

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