My wife had a very slim figure and didn't begin her periods until she was almost 19.
If you are slightly built or underweight you are likely to begin your periods later than average and if you have enjoyed good nutrition throughout your life so far and and are physically well developed and have a good level of physical fitness you are likely to start earlier than average...
As knowledge about nutrition has increased and the majority of the western population has had improved access to "healthy" diets, physical development has speeded a-pace and the average age of the beginning of menstruation has reduced from an average of around 15 or 16 of a century ago to what seems to be surprisingly young ages...
In the last few years I have read of a girl of seven starting her periods and a girl of nine successfully giving birth...
The trend is downwards and I think it is sad that young girls who should still be enjoying childhood have to be bothered with such womanly things - it is a bonus for any girl who starts later than average as long as she is otherwise enjoying normal development...