Further clarification on the meaning of "public" in this context:
Stuyvesant accepts less than 3% of applicants, making it about three times more exclusive than any Ivy, Stanford or MIT. The average SAT score is roughly in line with that of the accepted student bodies of top-ten schools — in effect, Harvard could close its eyes and accept 100% of Stuy applicants and do as well or better than with its normal applicant pool, at least with respect to standardized tests.
Stuy is not typically what you think of when you think of a "public" school.
They key distinction is that most schools of that caliber are very expensive. Stuy sits in a class alongside Hunter College High School and a few others with the relatively rare property of being like $30k+/year institutions while also not charging tuition.
Stuyvesant accepts less than 3% of applicants, making it about three times more exclusive than any Ivy, Stanford or MIT. The average SAT score is roughly in line with that of the accepted student bodies of top-ten schools — in effect, Harvard could close its eyes and accept 100% of Stuy applicants and do as well or better than with its normal applicant pool, at least with respect to standardized tests.
Stuy is not typically what you think of when you think of a "public" school.