Neither Anne or Andrew pursued higher education. Edward recieved a degree, coming fourth in the family (after Charles, and the two Gloucester brothers)
And I would dare say that if Anne had gone to university, and if she'd felt she could pursue a career back in the late 60s/early 70s, I'd bet my socks that she'd be a PhD in the end. She's one smart cookie, and whatever field she chose, she'd have mastered it completely and been successful as an academic. In a sense, her life was wasted because she had the door wide open... but you have to respect her for her dedication to duty and the fact that she made damn sure her kids weren't useless. God bless her.