Try hoopdata.com. They might have what you're looking for.
I don't think there is such a site.
The "average" player actually wouldn't exist because you're getting different things from the average point guard compared to the average center.
What you could do though, is got basketball-reference. They have the stats for the average team. Then you could calculate it per 36 minutes per player from there giving you a kind of theoretical average starter.
espn.com will give you every players stat lines. or if you just google "Kevin Durant stats", a million sites will come up
I just published it!