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:
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!