meanmeans.markdown

The arithmetic mean is a tool of the oppressor

Note: This argument is... not exactly tongue in cheek. I believe it, but I possibly don't hold this view quite as strongly as I'm putting forth.

The problem with the arithmetic mean is that it gives you a view of a population which does not in fact reflect the experiences of any individual member of it.

This is particularly problematic in distributions which are "peaky" in the sense of having their mass concentrated towards the high end of the spectrum. Such distributions are common: In particular power laws and log-normal distributions (log-normal distributions being what you get when you have a large number of small independent multiplicative rather than additive effects) both have this property.

When you apply the arithmetic mean as a way of gauging these distributions you are oppressing the disadvantages.

Why?

The answer is two-fold:

1. The arithmetic mean does not represent a true spectrum of the population. What it represents is the population weighted by importance, where "importance" is the measure you are currently considering. In particular it is often higher than the median by some margin. Most of your population will never experience life as good as what you are claiming to be the "average" experience when you use the arithmetic mean. Thus by making this claim you are lying to people and telling them that things are better than they actually are
2. When you make the mean the focus for improvement, the improvements you will get are going to be ones that benefit the people who are already well off. Why? Because most improvement is multiplicative. If you can make 100 peoples' lives 5% better, which 100 do you choose? If you're trying to optimise the mean, you pick the 100 best off. Why? Because the amount the mean gains is 5% of the total current value of the 100 people you've chosen. So you want to pick the 100 people with the total value.

In conclusion, the mean is a tool for telling the oppressed that things are better than they are and prioritising the gains of the people who the system already benefits. By measuring population means you are contributing to the oppression of the disadvantage. For shame.