sorry to hear your son broke his arm, and went undiagnosed for over a week

In my experience with broken arms (2 kids) it really depends on the severity & type of fracture that needs to heal.
My son was the first to break an arm, but it was quite severe so he was casted for nearly 3 months, and in a splint for another 3. That is not typical so don't worry yet.
My daughter broke her arm (forearm) and was only casted for 4 weeks (not a severe break at all). The second time she had a compression fracture of the growth plate of the wrist and was only in a splint for 3 weeks.
I do believe it has to do with how severe and what bones are actually involved in the break to determine how long a child will be casted. Younger children tend to heal quicker than older children. The average time for a cast is 4-6 weeks, again based on the severity of the break.
Hope this helps a little. Good Luck and SPEEDY healing to your son
Angela