Because of the way light is reflected, there are two isosceles triangles in the
diagram (equal sides are shown in red and blue). By symmetry, the length
of mirror you need to see yourself top to toe is at least half your height. It
does not matter where you stand as long as the mirror is hanging in the right
place on the wall. The top of it should be level with half way between eye
level and the top of the head (or higher) and the bottom of it should be half
way between foot level and eye level (or lower).
For a mirror to work for everyone, the bottom of it must be half way
between foot level and eye level for the shortest person and the top must be
half way between eye level and the top of the head for the tallest person. So
we need to know some measurements for the shortest and tallest people that
are likely to use the mirror.
American data is available here: http://www.cdc.gov/nchs/data/ad/ad361.pdf
The 95th percentile for heights of men is about 75 inches  190 cm.
The 10th percentile for two-year olds is about 33 inches  84cm.
Assume the distance eye level to the top of the head is about 10cm.
The bottom of the mirror needs to be 0.5(84 – 10) = 37 cm above the ground.
The top of the mirror needs to be 190 – 5 = 185 cm above ground.
A mirror 185 – 37 = 148 cm long will suffice if positioned as above. Most full length mirrors are shorter
than this so cannot be hung so as to cater for both tall adults and small children.