I saw an interesting tweet earlier in the week from Atrin Assa:

@nntaleb demonstrating central limit theory by adding together increasing numbers of individual uniform distributions. By the time you add 3 uniform distributions, the resulting distribution looks like a normal distribution. Beautiful. #RWRIpic.twitter.com/7guT0c4dig

I thought the idea would make a neat project for the boys today, and it turned out to be even more interesting that I expected.

I started by just having the boys look at draws from a uniform distribution. You never really get a chance to go back and see ideas like this for the first time, so I’m always really interested to hear how kids describe what they are seeing:

Next we looked at the average of two draws from a uniform distribution. The boys had different thoughts about what this would look like before we saw the outcome – that was fun to hear. My younger son had some interesting intuition based on a dice game he’d played previously:

At the end of the last video my older son wanted to check what would happen if we looked at the geometric mean rather than the arithmetic mean. This idea wasn’t what I was planning to study, but it seemed like a great idea so we tried it out. They both had interesting guesses at what this new distribution would look like:

We wrapped up today looking at the arithmetic mean and geometric mean of three draws. With the arithmetic mean they started to see the normal distribution appearing. With the geometric mean they didn’t recognize the shape – my guess is that they’d never seen a distribution like this before:

This was a really fun project. Nassim’s intuition about how to explain important ideas from probably and statistics is incredible. I love working through his ideas with my kids.