A person gave bags of jellybeans to 11 students. The mimimum was 8 maximum was 21, mode was 14 and median was 15. What was the number of jellybeans each student could have reported to get the landmarks given

Using just the data given, we can start out with a list of 11 ascending values fro min to max, with 15 in the middle:

min, median, max:
8 x x x x 15 x x x x 21

Now add some 14 values, so 14 is the most frequent value (mode):

8 x x 14 14 15 x x x x 21

There can be as many 14's as you want, from 2-4

Then fill in the other x's as you see fit.