Average is a good benchmark especially early in a tournament. Later in the tournament it is more about your stack size compared to costs, costs being blind and antes, and how many players are at the table to modify the costs. Dan Harrington in his tournament books calls this scoring "M's". The very general conversation about "M" score is the lower the M the more aggressive and desperate you should play your stack. The higher your M the tighter you can play your stack.
Exactly what you should do with any particular M at any particular point in a tournament varies widely, depending on other factors such as other players M's, players left in the tournament, players tendencies Etc. M in itself, is just a simple scoring system, a sort of short hand for discussing tournament tactics. Rather then going through player A had 100, T-chips, I had 20 t-chips the blinds were 5-10, one can discuss it like I had 1.5 M, villain had about 7 M at the final table were the average was about 5 M.
After reading Harrington, I started thinking in M's during tournament play and it did help to simplify the whole process. I urge you to pick up Harrington's books on tournament play for more about scoring your position with M and the lengthy discussions he has.
Your particular M compared to other players in the tournament is a pretty good benchmark about how well your doing in a tournament. Of course the practicality of figuring every players M is a little tough, until the tournament is down to a few tables.