that isn't how the median works

median is the sample in the middle of the distribution (when it is treated as a sequence of samples ordered by their value), e.g. if you have sort(seq(dist))=[100$, 5$, 5$, 3$, 1$] the median is 5$

average is sum(dist)/size(dist), so avg * size(dist) => sum(dist)

in the example above that would be median 5, avg. 22.8, total 114, size 5

if you where to multiple the median by size you would have 25$ for the total value, which is very much very wrong

True, and yet 5 describes each in the set more accurately than 25.