If all the exams have normal distribution will the average grades to student also be normal distributed? I have data on how many got which grade in every course I have taken, but I want to know how many have A, B, C,..,E average. The problem is that I don't know which student got which grade, but it is safe to assume that the students who got an A in course xxx are more likely to get an A in course yyyy than the students who got an E in course xxx. Is it possible to say something about the percentage who got A in average when you have the data I have? If 10 percent got A, 20 B, 30 C, 20 D, 10 E, on average will more/less than 20 percent have B average? English is not my native language so please ask if you do not understand the question.