My friend Sally saw a report says that the average income in her neighbourhood is $75,000. Sally feels inferior, because her income is well below the neighbourhood average. Sally asks her neighbors about their income. Everyone she asks says their earnings are also below the neighbourhood’s average. They do a little research and come to learn that 98% of their community have below average incomes.
What?! I told you — averages are not to be trusted.
It turns out that 2% of Sally’s neighbours have astronomically above-average incomes, thus making the ‘average’ income higher than that of the other 98%.
Averages Are Not to Be Trusted on Their Own
Averages work well for data that is evenly distributed – data shaped like that bell curve graph you might remember from school. But when the data is asymmetrically distributed, things get tricky.
Take, for example, a neighbourhood with a population of ten people, where nine of them earn $100 per year and one of them earns $10,000 per year.
In this example, the average per capita income is $1090 (10,000 + (9*100))/10).
But 90% of the population actually make about 90% less than this.
If the data is not well distributed — if there are way more people on only one side of the spectrum, or if there are some really big values at only one end of the continuum — then averages can not be trusted because they are not good indicators for an overall understanding of what’s so.
That’s when you should be looking for the median.
And What is a Median Again?
In fact, the median is much more like the middle than the average is. The median is what you’d get if you lined up all your measurements in order, from smallest to largest, and then choose the one in the very middle.
For example, if there are five houses on your street, the average house value is found by adding up all the home prices and dividing by five. But the median house value would be the price of the house right in the middle, with two more expensive houses on your street and two houses less.
So an unusually expensive house on your street would make the average seem higher than you’d expect it to be, but the median might align more with the amount that you would expect it to be.
If the houses on your street are a varied mixture of prices, in a more “normal” distribution, then the average and median will probably be closer together than in our first example where only one house was unusually expensive.
But even in this more balanced street, the median gives us a better idea of how most people in the neighbourhood are living.
Most people remember learning something about all this in high school math class. But if the way newscasters use the term is anything to go by, the only lasting impression from this lesson is a vague notion that the average has something to do with that place somewhere in the middle, and the term “median” has been forgotten altogether. And this misunderstanding can be used (intentionally or not) to skew statistics and distort our understanding of the facts.
It’s a common mistake. But a key thing to remember is simply this: the average is not necessarily anywhere near the middle. Sometimes it’s miles away. Sometimes it is about as atypical as you can get, and true of no one data point at all.
Statistics and mathematical terms can often be misused and misunderstood – sometimes by accident and sometimes to intentionally mislead us. Sometimes we ourselves may be guilty of presenting a false picture of our research because we don’t fully understand the mathematics behind the terms that are used.
As consumers, researchers and participants in the global conversation, it’s important for us to think critically — and to understand the words we are using in the first place.
Which leads us back to the assertion in our title: almost everyone has more than the average number of feet.
Think about it.
Want to know more about averages, data analysis or the average number of feet? Datassist is here to help. Contact us now.