Check to make sure the scope rail is mounted as tight as you can get it.
DO NOT do this. If you do, you'll probably strip the screw holes for the rail. The receiver is made of soft aluminum and the holes don't go very deep. You just want to tighten them to spec, which I believe is 15 inch-lbs.
As for your groups, I have a super hot rodded 10/22 that I have bedded in a way that I haven't seen any place that allows me to run the barrel full floated. This rifle, shooting its favorite lot of Eley Black Box will keep all of the rounds in 1/2" circle. Well, 95% of them anyway. Nobody's perfect all of the time. Today, while practicing for a 200 yard match that I have tomorrow, I shot several groups that were 1" and under at 100 yards, with the same lot of Eley. I'm just trying to give you an idea of what the rifle is capable of, while keeping in mind that it isn't any where near stock.
At 50 yards shooting bulk ammunition, my groups tend to run about 1 to 1.5". At one hundred yards, the groups more than double. If you really want to see what your rifle is capable of, without breaking the bank, get yourself some Wolf Match Target, SK Standard Plus or even CCI Standard Velocity. Even the worst lots of these will shoot better than bulk ammunition.
You should't let the groups that you are getting discourage you. It's about what I'd expect with a stock rifle and cheap ammunition.
If you aren't afraid to tinker, go over the rimfirecentral.com those guys are nuts about 10/22s. Check into pillar bedding the lug, bedding the stock and barrel and getting rid of that barrel band.