In this scene, Charlie has everyone spread out around the room to illustrate how their distribution is nonrandom due to their lack of clustering.

Charlie discusses how he inputs numerous variables to construct a database of fire "fingerprints" to trace the arson back to the perpetrator.

This scene illustrates how statistical models (especially concerning human behavior) can be wrong due to a variety of unforeseen factors.

In this scene, Charlie and Don realize that their mathematical model is wrong because they were focusing on the wrong factor (the home) as opposed to the right one (the criminal's workplace).

In this scene, Charlie explains how he checked the equations he's using to catch the killer by going backwards from his results and making sure he gets the same answer. Because he doesn't, he realizes that either one of his expressions or the data he was given is wrong.