A few other things to keep in mind: (assuming your other fundamentals are correct)

UP and Down shot strings usually means you need to work on breathing.

Shot groups all around the bull mean you need to focus on the front sight/sight picture more.

random shots to the left/right usually mean you need to work on trigger control and or not anticipating recoil. Along with this practice your follow through. You should have the same sight picture before and after the shot.

Also work on your position and aquiring a natural point of aim i.e. dont muscle the rifle to your body, position yourself so the rifle naturally aims/points at your target with little muscle effort. Slings and proper support help.

Just a few tidbits I've picked up when trying to diagnose my shot groups. hope that helps a bit. Have fun and stay safe.

This is some excellent info, thanks everyone.

I will be using this the next time I am staring down those evil paper targets.

Already, I can think back to recent outings and some of the problems I have had are explained exactly as I have experienced them.