According to interior decorator Carmel Maguire, the average person's eye line is right around 5 feet. To meet this average standard, she recommends hanging the mirror so that its centre is 5 feet from the floor.
Consider Users' Heights
According to Starcraft Custom Building, it is important to consider the height of those who will be using the mirror when determining how high to hang it. If most users are taller than average, the mirror should be hung higher. Hang it lower for shorter users. It may not be possible to satisfy everyone's needs, but height considerations can help you make the right decision.
The standard average height can be used as a guideline for how high to hang a bathroom mirror, but ultimately the decision depends on the users' needs. If you have small children, keep a step stool in the bathroom so that they can safely use the mirror.