Frame size isn't as cut and dry as saying that someone of a certain heighth should ride a frame of a certain size.
For example, I am 6"2.5 and I ride a 60cm frame. The guy that used to own the frame is 6"0. Last week I met a guy that is exactly my heighth and inseam size and he rides a 64cm frame. I know a guy that is 6'5" and rides a 62cm frame.
The only way to know for sure is to do a bike fit. Even with my 60cm frame, I have a 100mm stem. I like to sit upright and not stretch out much when I ride.