Answer
X is finite and can take values in $\{0, 1, 2, \cdots, 100\}$.
Work Step by Step
The highest average that can be achieved is 100, in the instance that everyone scores 100. Similarly, the lowest average that can be achieved is 0. Since the average is rounded to the nearest whole number, X is finite and can take values in $\{0, 1, 2, \cdots, 100\}$.
