Data and Displays · Challenge problem

A stem-and-leaf plot of $12$ values is $5 \mid 8$, $\ 6 \mid 2~4~7$, $\ 7 \mid x~y$, $\ 8 \mid 0~z~6$, $\ 9 \mid 1~3~5$, with each row in increasing order ($x \le y$ and $0 \le z \le 6$). How many different values can the median take?