I think a good player tries to get as much information as he can to inform his decisions, and your stack size versus the average stack size is very important. However, you cannot use it to justify a bad decision.
Early in a tourney, it's really not that big of a deal. I like to be above or at least no more than 25 percent below the average early. I probably don't start checking chip average regularly until after the first break. Then I will check just to see where I am. After the first break, I will start paying a little more attention.
In the latter stages of a tourney, chip stacks become more important. But again, you should never panic or get down just because you are below the average stack, and that's what I see in the OP. Deep in a tourney, I am generally okay if my stack is within 50 percent of the average. Why? Because I know that if I can win one all-in showdown, I will be right back at the chip average.
when your stack size gets smaller late in a tourney, what you should really be looking at it is how many BBs do you have? Let's say the chip average is 45,000, you have 20,000, and the BBs are 2k. You've got 10 BBs, so you've got time to be patient and wait for a good hand or pick a good spot. But if you have the same numbers and the BB is 4K, then you can't afford to be so picky.
The other thing to remember about the chip average is that way more players are below the chip average than above it. Late in a tourney, you will probably have 30/70 ratio - 30% above the average and 70% below it. So if you are just slightly below the chip average, you are probably still in the upper half of the field with nothing to worry about. Just be patient and stick to your game.