I've always been under the impression that FSU and USF have low average MCAT because they prefer non-trads with significant leadership, not necessarily because they can't attract such competitive applicants?
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This might well be, but as it relates to the overall perception of medical schools, the degree of competitive entry (see average Lizzy M scores of matriculants) DOES matter and generally dovetails/conflates with how residency programs perceive MS4 applicants. Some residency PD's say that they pay relatively little attention to the medical school of the applicant, but there is an element of PC in that...just as in saying that, "Step 1 scores are just one of many factors that we consider." If you have a 230 Step 1 (just above the 50th percentile), you likely cannot even get an interview for Ortho, Derm, Neuro, Plastics, ENT, etc.
Another aside...I find it interesting that MCAT scores have a fairly small correlation (~30% at most) to Step scores several years later. Spooky brilliant types (by definition, the exception among applicant pools-- medical students and later residents) are likely to smoke both, but Step 1 does measure what you soak up in MS1 and MS2, AND how well you can read/interpret myriad wordy questions over a 7 hour exam. As daunting as the MCAT can seem, Step 1 will become the most important/influential single test of a future doctor's life.
Generally, schools with high average Lizzy M scores of their acceptees will also have higher average Step scores and very solid match lists vis-a-vis competitive residency programs. This is why one might prefer to go to UCF versus FSU or USF, e.g...if one has the choice.