Differences in SAT ranges at top schools
Help me understand this. Caltech and Harvard both have Math + CR 75th percentiles of 1600 but the 25th percentile at Caltech is 1500 and the 25th percentile at Harvard is 1400. The 75th percentile is the same but there is a 100 point difference in 25th percentiles. Why? Does this mean Harvard relies more on "intangibles" for admissions decisions? That's a pretty big difference. The interquartile range at Harvard is 200 while the interquartile range at Caltech is 100.
Another example would be Dartmouth versus Tufts. They both have midpoints of 1445 (2015 data, I think) but Dartmouth has an interquartile range of 230 while tufts has an interquartile range of 150. That's an 80 point difference. I would think that Dartmouth and Tufts would be more similar in applicant pool than Harvard versus Caltech but there is still a big difference in SAT range.
Tulane has an interquartile range of 170 and UCLA has an interquartile range of 290. This is a 120 point difference. Yet they have the same SAT midpoint (1325).
What is going on? Do these big disparities in SAT ranges (despite identical midpoints) mean anything about the admissions process or applicant pool?
Why do schools with similar average SATs differ wildly in SAT variability among the student body?