How can I center a TV on a wall with a centered stud?
Measure the side to side of the back plate. I believe that most manufacturer's will have the plate long enough to span 2 wall studs. (BTW: most wall framing is established at 16 inches on center or 14 1/2 inches in between 2 wall studs). If your plat measures at least 16 inches install it on the 2 studs closest to the center of the wall. Some TV wall mounts have 3 axis' of adjustment: one axis allows you to swivel the TV side to side. This makes it easier to orient the TV on the center if the mounting plate was not. Also, it may be possible, depending on the mounting plate type, to offset the bracket that attaches to the back of the TV so that when it is hung on the wall mounting plate it is closer to room center.