Why do we need the "mean" in mean free path? I was introduced to mean free path in my astro physics class, 
and the professor posts a question for us to ponder: "Why do we need the "mean" in mean free path?"

This further makes me to wonder what is the mean free path for, and how is it used?
In every context we talk about "mean free path", we talk about particles. Particles usually bounce around a lot, from collision to collision. In between two bounces a particle moves in a straight line. That is the expected behaviour from Newton's laws of motion.

Between one collision and the next, a particle therefore moves a distance. That is the "free path". So why do we need to include "mean"? The thing is, you can never be sure about how far the particle moves after a collision. It might as well immediately bounce into another particle, as well as move a considerable distance. However, if you measure really many particles, their average is going to be pretty stable and predictable. That gives a nice, usable number. The "mean" here is for average. (In case you wonder, yes, this applies to optics too, but the concept requires a little more abstraction).