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Texas is still west of the current center and there has been huge migration to Texas.

Anecdotally a lot of that is coming from California, though, which would have no net effect on the median line, right?

Depends on how much of the California influx is coming from Bay Area vs. L.A. or San Diego. It could still be a net southern shift.

Fun fact: All the major cities in Texas are further south than even LA.

San Diego -> Dallas is a tiny northern move, though.

This assumes the data is granular to the city level. ...it's probably just state level data - and they are likely just using the state center point.

Texas has a big population, as does California so I'd be surprised if the (actually small) net migration from California is really meaningful.