For the data 2, 4, 4, 5, 10 the mean is 5 and the median is 4. Change the 10 to 100 and the mean becomes 23 while the median stays at 4. Why does one summary move so much further than the other?

D. Because the mean uses every value's size and the median only its rank.

The mean sums the values so every magnitude enters, while the median asks only which value sits third, and the fifth being 10 or a million does not change that. Neither behaviour is a defect: mean salary times headcount is the wage bill, and the median is the typical case. Nothing is being excluded; the 100 is counted as one value among five and simply not asked how big it is.