Central Limit Theorem

When you repeat an experiment over and over and add the results, the probability distributions change in an interesting way.

One Six-Sided Die

This distribution doesn’t look anything like a bell curve, but it does have a mean (μ\mu) and a standard deviation (σ\sigma):

Four Dice

Now we have something that looks a lot like a bell curve. Here are the mean and standard deviations for x\bar{x}.

Notice that the middle hasn’t changed, but the results are only half as spread out.

Ten Dice

Thirty Dice

Calculate μ\mu and σ\sigma for the average result of 30 dice.