For most people it happens when they graduate high school. I know that a lot of us keep rooms at home when we go off to college, but it's not like we live there. It's more a place to keep our junk until we finish college and can get our own digs. So, to answer your question, I guess a typical age to move out is between 18 and 22. Ish.
But, like everything else, there are always exceptions. Some people will continue to live at home after high school or college for any number of reasons, like to save money until they get a job and can afford their own place, or to help take care of an ailing parent, or because they aren't sure what their next step will be, and so on.
The bottom line is that every situation is different and everyone does what s/he has to do. If you have to live at home for a while and it works for you and your parents, more power to you. My only caveat is that it's very hard to date when you live at home, and the older you get, the more that your living under parents' roof can be a red flag to potential suitors. But if you have your reasons for living there, who cares? It's your business and your life.
I hope this helps. Thanks for the question.