Reconstructing dataset given mean, median and Stdev

[ruberhelios]

Wondering if it is possible to reconstruct a dataset if I give you the mean, median, standard deviation and N of a dataset.

For example, if there are 20 students in a class. The mean of their exam score is 80, median is 85, standard deviation is 14. Of course the maximum score for the exam can only be 100 and minimum zero. I can also further tell you that one student got 96.

Is there a way to reconstruct an approximate dataset to reflect these conditions? Thanks for your attention!

 

[mathman]

In the abstract you have 20 variables and only a few equations, so there are many possible solutions.