Character profile is over four years old and in the process of being edited. Apologies, stay tuned.
tl;dr: Ozma was a clever, creative Gryffindor, somewhat selfish but sufficiently outgoing. Her sister Emmaline was four years younger, somewhat less clever but athletically gifted, and attended Hogwarts with her. Ozma died at the age of sixteen in the year 1897, on Hogwarts grounds. But it was meant to be Emmaline.
This curious mistake left Ozma trapped as a ghost. Never given the opportunity to pass over, she has remained so ever since.
She is infinitely displeased with this state of affairs.