If he wants to get into a top MBA program, you should also think about where he wants to work after he graduates undergrad. Most of the top programs want at least a few years of work experience in their applicants. He also could consider becoming a CFA, etc. These aren’t decisions that need to be made now, but I’m just putting them out there to remind you that it’s not a single pipeline from BA to MBA and there are a lot of other factors your song can and will control.
As for the info you requested, I think your best chance is to contact Rice admissions and ask if they know how you might access those statistics.