What do you think of this math problem?

I thought of this one while stuck in a traffic jam. There was a story on the radio that said that teachers were striking because their pay was below the national average. That got me to wondering if the national average included their salaries. Would it be possible for their salary to be below average when their salaries are not included but above average when included? I hope that your intuition says that this is not possible. Can you come up with an argument to prove this assertion?