I wonder if average height is what we should be looking and comparing up to. It is after all a really arbitrary measure,and one should remember that it takes into account both the shortest and the tallest people. Shouldn't it be better if we look at a range of heigths that fits a certain percentage of the population.
The average is whithin the norms but not "within the norms",and very few people would be actually of the exact average.
It would be interesting to look at the most frequent height, though - it would be much more informative.
For example with my 176cm (don't know how much that is in feet) I am above the average female height of my country, but It is not above the normal height for women here.
nerd alert:
If I remember correctly from my research, the average height in the middle ages was nearly the same as now(few cm's shorter). Then at later times (mostly 18-19th century) it was generally lower.
Those suits of armour in many museums look short, because of the way they are assembled by the curators, which barely reflects the way the armour would sit on a living person.
The codpieces were used as a symbol. In some parts of Europe women did the same thing with their butts.
/nerd alert