My younger son wants to learn more about statistics. I’m excited to come up with some projects, though our journey here is probably not going to look like a typical statistics class.

My first idea was to have him investigate coin flips and look at similarities and differences with 10, 100, and 1000 coin flips. But really before we even got started he had a really interesting question.

So, here’s how he described the program I had him write ahead of time, and then we discuss the question he had -> In 100 flips, why did it seem that the chance of getting less than or equal to 50 heads was more than 50%?

To start diving in to his question, we first looked at sequences of 100 flips to get a better sense of what was going on. Interestingly, on a test look at 10 sequences, we did find that 6/10 had less than 50 heads:

Now we looked at the distribution of heads in 100 flips using Mathematica’s Histogram function – it was really interesting to hear him describe the different distributions that we saw:

Finally we talked about why my son was seeing what he was seeing in his coin flip program.