Helping kids understand when the Central Limit Theorem applies and when it doesn’t

My older son is studying a bit of introductory statistics right now. I was a little surprised to see this statement in his book:

“. . . you will learn that if you repeat an experiment a large number of times, the graph of the average outcome is approximately the shape of a bell curve.”

I certainly don’t expect middle school / high school textbooks to be 100% mathematically precise, but a little more precision here would have been nice.

For today’s project I decided to show them one example where the statement was true and one where it wasn’t.

For the first example I chose an exercise from the book -> the situation here is a basketball player taking 164 shots and having 64.2% chance of making each of those shots.

Here’s our discussion of that problem (sorry that we were a little clumsy with the camera):

Next we revisited the archery problem that we studied previously. Here’s the problem:

Sharing an advanced expected value problem from Nassim Taleb with kids

Here’s our discussion of this problem today. It is fascinating to see that even with 100,000 trials both the mean and standard deviation of the outcomes jump all over the place.

I think it is really important to understand the difference between these two different types of experiments. Both situations are really important for understand the world we live in!


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