re: engineering, maybe this is of interest, though a few years old:
http://profiles.asee.org/profiles/8046/print_all
http://profiles.asee.org/profiles/8048/screen/1?school_name=Vanderbilt+University
https://profiles.asee.org/profiles/8138/print_all
Entering class admissions stats are included. But you may have to get Cornell SATs from the 2017 posting.