The bottom line is that there is no surefire way to determine objectively whether a given kid is going to succeed in an engineering program. There are too many factors and kids are changing too rapidly at that age, so what might be true when they are 18 and graduating high school may be totally different a year later after their freshman year. Better “stats” likely has a positive correlation with higher odds of succeeding, but it is far from foolproof. I’d be willing to bet that better stats also has at least a loose correlation with struggling early due to bad study habits, as a sizable portion of those high-achievers got used to just skating by in high school (count me among that group).
The bottom line is that, if engineering is what someone wants to do, don’t let stats be your determining factor, either in the affirmative or the negative. Set a goal (e.g. of earning an engineering degree) and make it happen.
My son went to Univ of Rochester, graduated with Mech Eng degree. You simply declare your major end of sophomore year if you have over the minimum GPA . He had been accepted to RPI but the gender issue of so many more males to female was not what he wanted.
UR is big into research so contrary to what @KLSD wrote regarding smaller engineering programs and research, that would not apply to UR.
The benefit of UR is that there is plenty of space in the curriculum to minor in another areas as well as do a study abroad and still graduate in 4 yrs.
WPI has an active educational process offered in the freshman year to declare your major. One is not wedded upon admission to a particular major, but encouraged to make a choice before the sophomore year as there is a good deal of program planning involved for this project based system. A PDF of the process can be downloaded @ https://wp.wpi.edu/cdc/2014/10/10/brace-yourselves-major-declaration-deadline-is-next-term/
I want to second the Georgia Tech recommendation. My DD is graduating from there as an ME major in 3 weeks. Had a wonderful experience and got dream internships and full time job while having the typical college experience (big sports, Greek, study abroad, etc.). GT is working on gender numbers by admitting more women. I was just on campus and saw plenty of happy students. They work hard but with good time management, student can have time for fun. My DD got lots of support to succeed. If interested in GT go visit and get to know your local admission rep.
I also remember SMU, LSU and Tulsa being direct admit with good merit scholarships.