I had a back tooth extracted is it ok to leave the space there?

It depends: That's a very tough questions to answer because there are too many variables. That's what dentists are for. They don't just do the work but they help people decide what's best for them.

Probably not: Think of your mouth as a finely tuned machine. Remove one of the parts and you start to mess things up. You are young and by removing a tooth your teeth are going to start to shift. This can set you up for additional problems in the future. Try to get it replaced.

That depends: Often, back teeth are extracted without significant consequences (wisdom teeth / third molars). First and second molars however, are important chewing teeth and support each other as they function as well as support the size of the bone that they are in. Loss of back teeth could negatively affect the remaining teeth position, stability and function and, can even affect the jaw joint (tmj).

Maybe: It's hard to answer this question without seeing your x-rays and doing an exam. But in general, with the exception of wisdom teeth, every tooth in the mouth has a role. So if you lose a tooth, you should replace it. Also, a space may affect your other teeth, your bite, your jaw joints, and overall chewing function. Consult your dentist about this.