It's too varies to give a definite answer. Many people who hunt may not shoot for recreation, many who shoot for recreation may not hunt that often. Then you have folks who hunt only one type of game, and those folks who hunt various types of game, and those who do everything (hunt and shoot) year around. It's really hard to say what's average.
As many rounds as you think you need to stay proficient and enjoy shooting is what I recommend. For you to decide, it's your call.
Personally I lose count. I shoot for many reasons, but mainly for enjoyment and to stay proficient. I reload for my biggame rifle and I hunt. I shoot many rounds of trap and sporting clays with shotgun per year. I also use my shotguns for upland bird hunts and waterfowl hunts too. I plink with my .22LR, but also sometmes hunt small game with it too. I stay sharp with my many handguns, for defensive purposes, not hunting. All different types of ammo and guns for different reasons, too many to keep track of. I do maintain accurate round counts for all my pistols and for my big game rifles, but not for my .22LR rifles, nor any of my shotguns.
Historically, hunting has been a sport that has been predominately participated in by men. There have been notable exceptions, of course. Eleanor O’Connor, wife of the famous hunter and outdoor writer, Jack, traveled with him and hunted in many parts of the world, taking her share of game, including some exceptional trophies. Not as well-known to hunters today were Martin and Osa Johnson of the early to mid-1900’s. Together they traveled to many places that seemed extremely exotic and...