Mean is the sum of all incomes, divided by the number of households.
Median is the income of the household right in the middle of an ordered list of household incomes.
So, if I'm the median person, and my salary remains unchanged, but those above me all get raises, and those below me do not, I'm still the median, and median line would stay flat (even though the mean would rise, as you point out). So, the median actually has to rise for the graph of the median to rise, so the rise is real in terms of median.
I am fully prepared to admit that I am missing something, so feel free to correct me.
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