I define a person's genealogical center of mass to be the location whose latitude and longitude are the mean of the lat/long of his mother's and father's birthplaces.
My mother was born in Lakeside Hospital, Cleveland, Ohio at 41.505 N, 81.606 W, and my father was born in a company house in Dabney, West Virginia at 37.812 N, 81.928 W. That averages to 39.659 N, 81.767 W, which, with the help of Google Maps, is found near McConnelsville, Ohio. I was actually born about 170 miles north of there.
I don't even want to guess where my kids' genealogical COM is. Probably somewhere in the Pacific Ocean.