If you Google “Common Data Set” for each school on your list, you will find a document that gives a lot of admissions info on the school, including test score ranges. They typically give the 25th to 75th range. Post 28 explains that. Even if your grades are very good, test scores are what allow schools to judge across their applicant pool. Also, lower percentage students are often “hooked”
(athletes, legacies, URMs) – so they take up a lot of the lower percentiles.