I saw a nice video from Nassim Taleb today:

In the video he’s reference some of his earlier work that was really eye-opening to me. Specifically the discussion around 8:50 in this video:

Tonight I had the boys watch the new video and then we discussed the property of heavy tail distributions that Nassim talked about -> especially that the sample mean for heavy tail distributions is likely going to be below the true mean.

We started with some basic ideas from Nassim’s video and then looked at the alpha = 2 case:

Next we looked at the alpha = 1.2 case. Here we began to see clearly how the sample mean underestimates the true mean of the distribution:

Finally, we looked at the alpha = 1.03 case that Nassim mentions in his video and found that almost always the sample mean underestimated the true mean. We also saw that even with 100,000 samples, our sample mean was not even close to the true mean of the distribution.

This was a fun project. A little on the advanced side for kids, but my main hope is that they start to appreciate that an important part of any statistical analysis is understanding the kinds of distributions that you are likely to be dealing with.