It would depend on the act being punished, the person being punished, the one doing the punishing, and when and where, too. In the US, switches are out of fashion, along with corporal punishment in general, although it still happens in the home. However, that's fairly recent, in the last 40 or 50 years. Before that, a cane or switch might be used on the back, hand, legs and calves, or buttocks.
A girl, being tender and fragile, is more likely to have her hand punished, especially if her wrongdoing involves the hand, such as touching or taking something which was not hers to touch or take, or her legs, because baring the leg would be fairly shocking in most places and times (until shorter dresses were worn in the 20th Century), yet not be striking an overtly sexual part of the body.
Boys are expected to be able to take more pain, especially repeat offenders, and while they might be hit anywhere, were more likely to be struck on the back or buttocks. The "rule of thumb" disallowed switches larger than the thumb, as they could cause real damage.
Maryn, semi-knowledgeable