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Fooled by the ‘Average’
An Analysis of UK Income Distribution
Despite what the photo might suggest, we’ll be looking at the UK income distribution data from 2020. If you want a link to the original source, here it is!
I want to discuss how statistics can often paint a false picture if they are not fully understood, and I thought I’d start with the ‘average’, which most of the time refers to the mean. If you’re interested, do also take a look at my next article in this series as well: Fooled by Standard Deviation.
Definition
The mean is the weighted sum of probabilities of all the possibilities in a distribution, where the weights themselves are the numerical values given to the possibilities. For example, given a coin flip with possibilities: {heads: 0, tails: 1} and probabilities: {0.5, 0.5}; the mean/expected value of the coin flip is:
The Mystery of the Mean
Generally, when we think of the average value, we consider something like ‘the middle’. Let’s bring in the example of UK income distribution now. A quick Google search for “what is the average salary in the UK 2020” gives the following result front and centre:
Given this result, you might think that if you earn £38,600 around 50% of people might earn more than you and 50%…
