One of the reasons for writing this blog post is to help people make sense of numbers – the other is because my family is tired of listening to me. The biggest bugbear in my life is how we use the average as a measurement when it not only tells you very little but also hides the real story. Journalists particularly should work on their number literacy, because they are often guilty of using numbers incorrectly for clickbait and sensation purposes.
We are all familiar with how to work out an average – Average = {Sum of Observations} ÷ {Total number of Observations}
How often have you seen statistics like the following: the average life expectancy, the average wealth, your child’s average test score? All pretty useless in my opinion.
Average life expectancy works very much on for everybody winning, somebody is losing. What it does not mean is that everybody lives to approximately 47, 66 or 80 years. What it does mean is that if you have a relatively low life expectancy, the first question you need to ask is what is the mortality rate for children under 5? Often what you find in these cases is that you have a high child mortality rate, but once you pass the age of five, you live until old age.
Average wealth is another one that often gets skewed by outliers. If we all share a room with Jeff Bezos, the average wealth in that room would be something we all wished we had!
The last one I find particularly problematic because it gives you a false sense of ability is average test scores. Average does not make provision for outliers- it calculates it as a normal occurrence. Your child performed well in four of the five tests, but on the day of test number five, she is completely off her game. Perhaps her dog died or her tummy is upset or she had a fight with her best friend. Averages do not treat this as a once-off but still bundles that once-off performance into how we view her overall ability. One bad day should not have that much power.
Statistics has several other measurements that are way more useful than average in certain instances. First off, statistics doesn’t use the word average – they call it the mean – exactly the same thing. The two most often used measurements are the mode and median. The mode is the most common number and the median is the middle of the set of numbers.
Let’s go back to the examples above and apply the mode or the median. Would it not tell us much more about our average wealth if we stated how much most people were worth or which person’s income fell in the middle? It is giving us a clearer picture than average. The reason statisticians came up with these two measurements is that they wanted to get away from outliers. They wanted to not include Jeff Bezos or your child’s bad day.
It is important to understand what we want to answer to understand which measure we want to use. Let’s go back to our question on life expectancies. Mode is the most common number in a data set, so if you had five women and their ages are 22, 36, 80, 80 and 92, the mode is 80. This will be a much better indication of life expectancy because it doesn’t get skewed by outliers (i.e. infant mortality, people that live to 100, etc.). This also has loads of practical implications, e.g. financial firms used this to assist in retirement planning, etc.
Here is where I have a huge bone to pick with journalists that often use averages when reporting on planning, welfare assistance, etc. The only people more misleading would-be politicians who use the wrong measure to make themselves look good. There are ten children in your school that come from vulnerable communities and require school lunches. One child, however, has an apple tree at home and comes to school every day with twenty apples. The average child has 2 apples – and that is what gets reported, but if we use the correct measurement (median), the pictures look far different and way more realistic. The median child has no apples. The median child needs help. Pronto.
So next time you see an article that tells you the situation has improved and the average wealth/support/ownership/whatever has increased, look at that data with suspicion. The average very seldom represents the majority of us.
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