At a small high school, the 12th grade is only 20 students. They all take the same five classes (English, Math, Science, History, and Latin) together. At the end of the year each student is assigned a numerical grade between 0 and 100 for each class. Obviously, to calculate their gpa for the year, a student adds their five numbers and then divides by five.
The median grade for each class is known, but nothing else. We cannot even assume that the grade distributions in each class are normal. Can one draw any conclusions about the median or mean gpa?
If concrete numbers helps, pretend that the median grades are: English: 83, Math: 84, Science: 85, History: 86, Latin: 87.
