A set having the same mean, median, mode, and range Is it possible to have a set with the same mean, median, mode, and range?
If not, how can the following question be solved:

Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.
Using the above information, indicate which one will be greater:
a) the smallest possible number in set $H$.
b) 6.

If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.

Hint:  If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them.  To have a mode you need duplicates), $\{2.5,5,5,5,7.5\}$ satisfies the constraints.  Can you modify it to use only integers?
