Have you seen this map, which shows the geographic center of the USA and also plots the current median and mean of the population? Very interesting! I got it from another math teacher, but I think the original source is the US Census Bureau (that’s what the bottom of the file says at least!). It inspired me to do some more poking around, and in the wikipedia article I found this map of how the population mean has moved over the last two centuries. Cool.
And of course, here’s the median’s movement over time, too: