There are two sections of an introductory statistics course. Section A has 25 students and section B has 30 students. All students took the same final exam. The mean score in section A was 82 and the mean score in section B was 78.

a. Find the sum of the scores in section A.

b. Find the sum of the scores in section B.

c. Find the mean score for all 55 students.

d. The average of the means in the two sections is (82 + 78)/2 = 80.

Explain why this is not equal to the mean score for all the students.