I am 5'5 and weight 9 stone 2 my weight fluxuates between 8 stone 10 and 9 stone 6 is this average for a fifteen year old girl?

I think, I'm about the same height but a few years younger and I weigh 7 stone.
Yeah your weight is fine, don't forget you need a bit of fat to insulate you. I am same height, 8 stone 5 and slowly rising. I used to be like 7 stone 9, but I hardly ate anything so I tried to eat more and gained weight. As long as you're at a healthy weight and your lifestyle is good, it doesn't matter. Your weight sounds perfect to me, though. My friend is a pound heavier than you and a bit shorter I think and she's got a great figure.