Number Theory- Mr. Mendez's class problem

Since this is the Counting and Probability forum, I would like to begin with the fact that this is not the normal counting (1, 2, 3...) you may think of. By counting, I mean to introduce concepts such as casework and number theory.

First question I would like to introduce:
If Mr. Mendez awards extra credit points to his students with quiz grades that exceed the class average, what is the largest number of students that are awarded extra credit in a class of 107?

(Note this comes from one of the easier questions of 1995 National Sprint MathCounts)