MarkS told us:

"Half the people in my district make below the median income." I actually heard a politician say this at a hearing in Washington, looking for more federal aid.

The politician may be correct, depending on the median he's referring to. I think you've assumed that he referring to the median of his district (which is a reasonable thought, I'll admit), but suppose he really means that "Half the people in my district make below the United States median income."   He might be correct but poor at stating what he means.

I tend to think that he's just muddleheaded, which I think was your point.

Dave Oesterreich