On Google Maps, if you put in directions to a state like Minnesota or California, it will put a pin somewhere in the state. In the beforementioned states, it's approximately the center, but it's hard to tell. I tested this by looking for directions to Hawaii. The pin isn't in the center, somewhere in the water, but on the southeastern island, and not even in the center of it. How do they choose the location of the pin of larger locations?
I haven't experimented with countries yet.
The center of Google's earth
is home to my orienteering club.
It's Google. It's not like anything's accurate on there. Stupid thing always sends me on driving routes through dead end roads.
The Rural City of Mildura (in political terms, roughly the equivalent of a county in the US) covers an area of probably 150 x 150 kilometres. The town of Mildura is in its northeast corner. In the early days of Google/Apple Maps there were numerous reports of people trying to get to the latter who followed directions to the geographic centre of the former, which is in a remote area of semi-desert sand dunes in the middle of a national park (and getting stuck in the process because the tracks out there are no place for anything short of a proper four-wheel-drive).
Cue other stories of odd Google directions. The Australian Champs this year were based on Bathurst. Bathurst has a motor-racing circuit which for most of the year is a public road. Accom on "Conrod Straight" should have been easy. But there are all sorts of other roads in the Google database with locked gates on them, possibly measures to ensure that petrolheads pay to park and view during races. Got us on arrival, got us finding our way out again:-)