Hermione went back to Hogwarts to complete her seventh year of study and her N.E.W.T.S. Harry and Ron did not.
J.K. Rowling:“She would definitely, definitely go back. And she would want to graduate, and I think that she was- I mean,I love Hermione. She went with Ron and Harry because she has a really good heart. That’s not about brain. Ultimately, she had a bigger heart than she had a brain and that’s saying something for Hermione. But did she- Was she naturally drawn to battle? No, she wasn’t. She’s not a Bellatrix. She’s not a woman who actually wants to be hurting, fighting, killing. Not at all. She would be glad to go back to school, be glad to get back to study, and then would join [Harry and Ron] at the Ministry.”