Grades on a very large statistics class are given according to the following dis

Question

Grades on a very large statistics class are given according to the following distribution:

A

B

C

D

F

15%

35%

30%

16%

4%

How can we find the mean grade given in that large statistics class?

Pretend there were exactly 100 students. How many should get each grade?

Compute the average grade for those 100 students.

This type of computation would work for any number of students, since the number of grades you add in the numerator must match the number of students in the denominator. In fact, you don’t even have to pretend to have any number of students. Check that you get the same answer of you use the following formula: µ = ? xP(x) The mean if a population is also called its expected value.

A

B

C

D

F

15%

35%

30%

16%

4%

Explanation / Answer

The mean grade can be found by taking the (summation of product of grade and % of students securing that grade) divided by 100.

For 100 students,

15 should get grade A

35 should get grade B

30 should get grade C

16 should get grade D

4 should get grade F

Average grade for those 100 students = (A*15 + B*35 + C*30 + D*16 + F*4)/100 = 0.15A + 0.35B + 0.3C + 0.16D + 0.04F

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