[throwaway2245]

I created a salary distribution as an example, with 30% of employees at half the median pay, that get "outsourced":

1 1 1 2 2 2 2 3 6 60

median moves: 2 to 2 (+0%)

mean moves: 8 to 11 (+72%)

(You can make your own example.)

Usually, you expect the median to be pretty stable when you remove (or add) outliers. That's often the reason it's used in formal statistics.