The best height for hanging wall pictures is the height that is good for you to enjoy them. For very tall people they would hang higher and for shorter people it would be lower. So, there isn't a hard fast rule except for you to choose what looks good for you in your home.
There really is no proper height when hanging pictures on the wall. It is generally up to the discretion of the person hanging them. Generally you would like the center of the picture to be at about eye level. This can vary greatly if you are staggering the pictures that you are hanging.
I think the proper height is eye level to the home owner. You want to be able to see the picture and not have to look up to enjoy your art. I stand back and make sure it does not look too high or low by having my husband hold it for me.