Hi 준비하다 means prepare, 준비 중 means preparing. simply when you say verb+중, it means you're in the middle of it or you're on it. it's similar to verb+ing but little bit different. I'm not a teacher so It's hard to explain exactly however..because 준비 is a noun while 준비하다 is a verb, and 중 is also a kind of noun that makes 준비 중 is two words..not a variation of 준비하다. and we usually put a space before a word '중'.

Yeah I agree, 중 is another word (see grammar 중이다) not a form of 준비하다. 준비 is a noun. 준비하다 is a verb. 중 is used to show something is in progress. (Ex. "Under construction"). Refer to that grammar point.