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It's the usual problem Rowling has with the number of students who attend Hogwarts. She said she assumes about 1500 students. This shines through in the mass scenes (Quidditch, exams etc.)
I personally agree with your 280+ from the evidence in the books, e.g. number of staff, students to be named and the total number of British wizards JKR mentions (3000). How could 3000 (adult) Western European wizards and witches produce so many children? BTW Hogwarts is still a public boarding school. The 1500 students JKR imagines, probably from her own experience at a state comprehensive, are simply not manageable. At my comprehensive school we had the same number of students with more than 100 teachers and still class sizes over 30.
I personally agree with your 280+ from the evidence in the books, e.g. number of staff, students to be named and the total number of British wizards JKR mentions (3000). How could 3000 (adult) Western European wizards and witches produce so many children? BTW Hogwarts is still a public boarding school. The 1500 students JKR imagines, probably from her own experience at a state comprehensive, are simply not manageable. At my comprehensive school we had the same number of students with more than 100 teachers and still class sizes over 30.