This is an example that I use with my kids to explain why the term “average” by itself isn’t meaningful, and why it’s a good idea to understand both outliers and clusters when looking at data. We start with the easy topic of averages and I ask them “Are we talking about the mean or the median?” and then remind them what the differences are:
- Mean – the mathematical average – sum all the values, then divide by the total count of values, and you have the mean.
- Median – the middle point of the sorted values. This is usually much more useful, especially with smaller data sets, or data sets where there can be extreme outliers.
- Mode – the number that appears the most frequently in a data set. It’s interesting, but not particularly useful.
I’m going to use the exact example that I share with them, because I can source (or I thought I could, turned out harder than I hoped!) some actual data to support it, although the data is a little old (2018, I’m writing this in 2021 and updated in 2023), the lesson still works.
According to this article from Ultimate Motorcycling, citing research from the Motorcycle Industry Council, the median household income for a motorcycle owner in 2018 was $62,500 (of note is that this is unchanged from 2014, and slightly down from 2012).
Accordingly to this Wikipedia page, citing the Forbes list of the world’s billionaires, Bill Gates was worth $90 billion in 2018. Now I think Jeff and Elon are worth more now, but no matter. And putting aside the fact that wealth and income are lowly correlated, we’ll just use the annual income of Bill Gates in 2021, which was $41B (assuming he donates or endows his charity with much of his income).
But you’ll see in a second that it doesn’t matter that much. There are plenty of biker bars up in Cave Creek, Arizona, largely because the drives to, from, and all around that area are just gorgeous. So let’s say Bill walks in on a Thursday night when there are 50 other people there. If their average household income is $62,500, we have the total income of the patrons in the bar before he walks in as $62,500 * 50 = $3,125,000. When Bill walks in, their income goes up to $41,003,125,000, which divided by 51 people is now $803,982,843.14. So if you wanted to sell a product to the “average” person in there, you’d still have a product that only one person could actually afford.
This is a dramatic example, but it actually really drove the point home to my kids. And them I showed them another example of how this works with choice and happiness and why when you stop looking for “average” and instead look for groupings or clusters. For the ultimate example, watch this TED talk from Malcolm Gladwell (also pasted below) summarizing a chapter from his book What The Dog Saw about Prego and how the clustering research on tomato sauces from Howard Moskowitz caused them to introduce a Chunky Tomato Sauce line, and earn them $600 million dollars over the next nine years. Turns out nobody likes an average tomato sauce. They want plain, spicy, or extra chunky. This area is called horizontal segmentation, and reminds us that clustering is generally a better way to think about consumer, or voters, or students, or most other populations.