While actual price varies considerably among individuals so that there’s no one way to compare costs and many do not pay sticker, 40% of undergrads at HYPM is not rare and outside of the handful of super elite colleges, most students do, in fact, pay sticker.
According to Harvard’s CDS 2014-15, about 56% of freshmen were receiving FA (lines d/a). For CDS 2007-08, the earliest year I could find, the percent was about 54%.
Princeton CDS 2016-17, about 59%. For CDS 2001-02, 39%.
Stanford CDS 2016-17, about 44%. For CDS 1999-2000, 38%.
Yale, CDS 2016-17, about 61%. For CDS 2003-04, 43%.
MIT CDS 2016-17, about 57%. For CDS 2003-04, 49%.
Even just barely beyond the tiny world of HYPSM, more than half pay sticker.
Penn CDS 2016-17, about 47% of freshmen received FA. For CDS 2009-10, 41%.
Brown CDS 2016-17, about 44%. For CDS 2004-05, 45%.
Cornell CDS 2016-17, about 45%. For CDS 1999-2001, 49.5%
Northwestern CDS 2016-17, about 45%. For CDS 2001-02, 43%.
Duke CDS 2016-17, about 45%.
WashU CDS 2016-17, 41%
USC CDS 2016-17, 33%
I did not look up every college. Here are two exceptions where (a little) less than half pay sticker besides HYPM:
Vanderbilt CDS 2016-17, 53% of freshmen received FA. For CDS 1999-2000, 42%.
Notre Dame CDS 2016-17, 52%. For CDS 1997-98, 40%.
In the even tinier world of elite LACs, there is also a high percent of freshmen receiving FA, similar to HYPM.
Amherst CDS 2016-17, 52%
Carleton CDS 2016-17, 55%
Swarthmore CDS 2016-17, 58%
Hamilton CDS 2016-17, 52%
But lower in ranking from the most elite group, percent of freshmen receiving FA falls off:
Skidmore CDS 2016-17, 39%
Lafayette CDS 2017-18, 36%
(Note, I am not complaining about having to pay sticker but merely pointing out that paying sticker is quite real for a significant portion of families.)