All in all, the point isn’t that schreyer is sorta jhu. Rather, the point is that Schreyer may be a better choice than NEU if JHU is the reference point but is too expensive.
(Note that I’m not affiliated with any of those three but am trying to look at OP’s daughter’s options.)
8% is the number I’d been given and I didn’t actually calculate that rate, it looked correct in terms of applicant/number of places. 20% is not bad even if it’s not as impressive :).
For the 4 md/phd freshmen, they don’t represent how many Schreyer students perform research (they’re ALL required to by junior year at the latest, and receive support). That program is a special program with Hershey and is open to students who want an md/phd. JHU does have an edge on that account though.
However on the matter of test scores, since those are explicitly NOT used to select students, to me it is quite impressive they’re high anyway. Keep in mind that this includes a variety of majors that typically aren’t part of honors programs or at jhu - I was surprised recently to learn that Schreyer includes elementary school majors, agricultural science majors, and basically all majors from all the possible schools - all students whose results are high for their group and bring a diversity of perspective even though.
As an aside regarding high -2100= top 2% -scores, which may indeed… or may not… matter to OP, I personally don’t think a student with 2150 and a student with 2200 are that dissimilar, but OP may well differ. Overall, JHU is higher ranked, there’s no doubt about it, and it’s top students would be top anywhere including Harvard or Stanford ; Schreyer students are those who were just below the Ivy threshold, really impressive but not at that ‘top 20’ level.
However it is highly ranked too (top 10in teh country, receiving massive respect throughout the Northeast, whether for academia or employers) - especially since it’s being compared to NEU.
(Schreyer scores are 1950-2153 and neu scores are 1960-2210 for instance. Keep in mind that NEU excludes internationals ’ scores whereas psu doesn’t, and that new selects students in large part based on scores, whereas Schreyer doesn’t.)
Is JHU worth 90k more ? OP may well decide it is. It IS a terrific school.
Anyway, the suggestion came after reviewing the list of possibilities and their costs ; it was related to the fact OP doesn’t really want to pay full price at JHU, and OP’s daughter isn’t sure she wants to be a pharmacist (which makes the NEU program a potential disaster) so NEU may not be the right choice either. Schreyer would thus be a good alternative to NEU without costing as much as JHU. (Even among students who are sure about being pharmacists after shadowing pharmacists there’s a drop out rate when students discover the job doesn’t have human contact the way doctors experience, that the job often is tedious, that it’s very different from what they thought day-to-day. Choosing your future job at 17-18when you have no clue what it’ll entail is risky, even for those who think they know what they want, so it’s even riskier if students are really unsure about their career path. ) Schreyer offers a good balance : much cheaper than the other choices, flexibility in choice of major, research opportunities, and a diversity of high - level students.
The one downside is that the daughter likes cities, and Penn State is in a college town. No skyscrapers that I know of. Lots of things to do for college students but it’s not central Boston. Only OP 's daughter can measure whether living in a college town is okay and whether it can be offset by the freedom to choose what she wants to study, or if living in a big city is more important than being able to choose her major and career.
If OP has decided he can pay for JHU the point is moot 
.