You need to use TOTAL, not Window_Avg for your calculation... This will avoid the average of an average problem.
TOTAL( AVG( [Score] ) ) will give the departmental average when you set compute using Program, and gives the program average when you set compute using Department. If you make two of these calcs and then a third that compares them, you can have a comparison
See attached for an example.
TOTAL example.twbx.zip 83.8 KB