What’s Average?

Today I said to Elliot, “on average …” (What I was talking about is not very interesting. Trust me.) Of course, Elliot immediately asked what average is. It turns out that describing average to a four year old is really hard.

My first inclination was to describe the function that is used to calculate the arithmetic mean of set of data. Elliot does not understand division yet so that was right out. Instead, I started to describe median. Median is easy to describe to a four year old and, as it turns out.

Before I had gotten very far into describing median I decided that I should probably answer the question Elliot has actually asked. So I finished describing median, then told him that what I had described was something call median which is one way of calculating average. Then I took a moment to think about average some more.

At that point, I realized that probability is the important part of average. I decided that a four year old could understand some basic probability. So, I describe how I am of average height and if we guessed that some man we had never meet was my height we would be correct more often than not because more people are of average height than any other height.

I felt like, while that description was true (particularly for the imprecise way four year olds figure height) it left out some important aspects of average. However, by this time Elliot was thoroughly bored with the subject so I let it go. I still don’t feel like I have a decent elevator pitch for average, and understanding average seems really important. For me, these sorts of situations are some of the hardest (and most interesting) parts of parenting.