That's a question with a lot of potential pitfalls. Ten yards is relatively close, so decent sized groups should be the norm. In fact a low powered, less-than-$100 Daisy 953 will probably shoot groups around half-an-inch at 10 yards -- scoped or unscoped.
There are at least three things to consider. First, not all pellets are created equal. Pellet rifles are notorious for being selective about what they can shoot well. Pellets come in different sizes (
e.g. head sizes of 4.50, 4.51, 4.52, even 4.53mm), different shape (round head, wadcutter, pointy, hollow point, gimmick), and different weight (light weight alloy, mid-range, and heavy). If you are using inexpensive Chinese-made pellets, for example, individually they may not be of consistent size, shape, and weight. Do not use light pellets, pointy pellets, or cheap pellets. Stick to quality round head pellets (or for short range, lower powered shooting, wadcutters) made by manufacturers such as JSB or H&N. (The Crosman pellets sold in tins at CT are for times when nothing else is available.)
Second, high powered spring piston air rifles can be very challenging to shoot well. A springer has a two-way recoil that is no friend of accuracy. The greater the power of the air rifle, more often the greater the difficulty of shooting it well. Ten meter airgun competition has always favoured relatively lower powered guns.
Third, and directly related to the second, is that it is necessary to hold and shoot a spring piston air rifle much differently than a PB rifle like a .22LR. The heavy recoil referred to above makes it necessary to use the "artillery hold" to minimize the effect of the two-way recoil. See
http://www.pyramydair.com/article/The_artillery_hold_June_2009/63 and
https://www.youtube.com/watch?v=fOYSU5Lq7oA
Many shooters unfamiliar with the peculiarities of shooting a spring piston rifle are often seduced by manufacturers' claims of power and high veloicities of 1100 or even 1200 fps. High power doesn't make any springer superior to another. Stoeger air rifles are made in China. They work and shoot. Don't be offended, but they and the many other Chinese-made air rifles available are the Norinco's of the airgun world.