Avast is an on-access, resident antivirus, so it isn't dormant, when you are using the system it is going to be active and using some CPU and RAM scanning your activity.
Do you have any other security based software installed on your system ?
The avast service (is the main avast service) and the Avast antivirus engine server
You say what you are doing when you see these figures (which I would say are higher than normal) ?
You don't mention anything about your system Operating System, RAM and CPU (other than "I've got a pretty solid processor") ?
You can look at my specs below my post and this is on a laptop so nothing spectacular, but I don't see this kind of activity. I'm not a gamer where I would expect it would get a better workout. Only browsing and compiling this post and effectively zero CPU activity by avast.