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.
Best Answer
The multiset $[3, 4, 5, 5, 8]$ will fit the bill.
You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).