The only time you can get an "average" depth, is 1) assuming an undisturbed site, (therefore, not furroughed fields, beaches subject to erosion and re-fill, places where gophers routinely turn over fields, etc...) and 2) comparison only within each site. Because once you move to another site, each soil type is completely different. So whatever answer someone gives here, for just one site, has absolutely no bearing on anywhere else, and is not an "average depth", except for just where he happened to be, at that moment.
I've gotten spanish reales and early seateds an inch deep before (hard pan dirt, demolition sites, furroughed fields, beaches after storms, etc...) And I've gotten zinc pennies 6" to a foot down (turfed lawns in moister sections, beaches on the spongy wet sand, dry sand, etc...)