Whilst I am unsure how genuine the op is, the debate is nonetheless interesting. My personal stance would be to work as hard as I could to get her to finish her formal education, whilst not ridiculing or belittling her.
To those of you advocating that she be able to make her own decisions, remember she is only around 15, as she hasn't even taken her GCSE's. At boarding school she will be leading a fairly sheltered but academically pressured life. I am sorry but you don't really know what your future career will be at that age, most children change their minds. As fee paying or non fee paying parents we want to give our children all the opportunities, academic and non academic, to achieve and choose what they want to do as they get older. We want to open doors for children not close them. I believe that it is my responsibility to my children to encourage them to go as far as possible with their education. Then the choice is theirs. They can be doctors or plumbers etc. but they can choose anything. If they choose to leave after their GCSE'S a large part of me would feel I has failed them. I want them to be able to achieve anything and contrary to some posters that is simply going to be so much harder if she leaves after her GCSE's, no matter how you dress it up.
I went to boarding school and at that age we were all desperate to spread our wings and ultimately rebel and test the boundaries. We would have probably jumped at the opportunity to leave after GCSE'S, what 16 year old wouldn't!I remember after my GCSE's seriously suggesting to my mother that I would like to work in Mcdonalds as I was enjoying my holiday job there so much. Whilst there is nothing wrong with that, aside from the fact that I turned vegetarian at university, I know now that I would have hated giving up school to work there! I am eternally grateful to my parents for facilitating my education, which allowed me the choices I have had in my life. To those of you that say she can go back into education, yes she can, but it's so much harder and being a mature student isn't the same experience on so many levels.
Encourage her to get a summer job in a salon. Talk to her, not down to her but seriously I would be pretty firm. My line would be if that's what you want to do after you finish your education, then fine I will support you all the way.