Is the average of group averages always equal to the overall average? Let’s make this question more precise: Suppose that an instructor teaches four sections of a course, and the average scores on an exam for the four sections are 77, 80, 83, and 84. Is it necessarily true that the average exam score among all of the instructors’ students is equal to (77 + 80 + 83 + 84)/4, which is 81? If not, under what circumstances would the overall average equal the average of the group averages?