Two basketball teams, Team P and Team Q, each played 8 games. The average points per game for Team P was 56, and the average for Team Q was 63.

Which of the following must be true?
I. The total number of points scored by Team Q was greater than that of Team P.
II. The median points per game for Team Q was greater than the median points per game for Team P.
III. At least one game of Team Q had more points than at least one game of Team P.