Data and Displays · Superchallenge problem

A stem-and-leaf plot shows $12$ values (stem $=$ tens digit, leaf $=$ units digit). Stem $1$ has $2$ leaves, stem $2$ has $4$ leaves, stem $3$ has $4$ leaves and stem $4$ has $2$ leaves, but the leaves themselves are hidden. What is the largest possible value of (mean $-$ median)?