I would not give my 10-11 yr old a 250cc quad to ride , too much juice and too much weight for such a child is my opinion.
Next let me say it also depends where the kid will be riding that makes a difference , we ride alot of hills and that type of thing around here mixed with trails threw the woods and my entire problem with the mid weight class of quads for kids is there is just to much power and weight for those kids to handle properly , and my concern is them getting them selves crushed , I feel the 2wd mid class quads stand up to easy for little kids, and they can tip to the side.
When I was deciding on a quad or dirtbike for my daughter , we went with a dirtbike , and alot of the reason had to do with , normally when you dump a dirtbike you end up rolling along the ground or only have the weight of a bike upon you , a mid weight quad can squash you alot worse , so we went with the dirtbike , now these kids tearing up the roadways and misbehaving is a different story and not something that was going to be taking place on my watch.
For the small cheap china man quads for little kids riding in a nice area I am in favor of , I don't like the china man quads for grown up riders actually using the machine as they cost to much that I say get a real quad for a little more and have a much better machine , but if little jr is going to tool around the back yard or an old ball field for a few years before outgrowing it , I say get a small chinaman quad .............. 250 cc quads for little kids? NOPE