How do I calculate my family's "average family location"?

So, I just listened to a This American Life podcast called Ghost in the Machine. In one of the stories, a man decides to calculate, every week, the Average Family Location of his family. By that, he means: once you add everyone's coordinates for every coordinate in which they've been in that period, what city/location represents the average point between them all?

I decided to do the same for my family, which will be much easier because there are no touring musicians among us. The one complication is that a good chunk of the family is on other continents, and I wouldn't want us to "meet" in the middle of the ocean. So some approximation might be warranted.

I'd be happy if someone could provide me the math, I'm fairly confident I would be able to do it with a calculator or maybe put into some crude Python. I don't think I need to make a weekly report, since we're not that mobile. Maybe twice a year, or once every two months.

Thanks!

Edit: I don't know much math

Edit2: holy shit this is not simple at all! Now I feel kinda bad for throwing this problem at you guys. I really thought it would be quick and easy!