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On average

October 4, 2007

A variation on lies, damn lies, and statistics.

Ever notice how sometimes politicians/pundits want you to pay attention to “average” numbers, calling no attention whatsoever to the distribution of values, and sometimes they try to make you feel like your case is special, and you are not average at all?

So, for instance, how often do you see “average” incomes or “gross domestic product” reported, and often often do you see income medians and income percentiles reported? They distribution of incomes has actually changed quite a lot in the last few decades, and members of the wealthiest few make hundreds of times more money than members of the many poor. But what gets reported most often, is the “average”. If the average is up, if the gross is up, we’re all doing good, right?

Compare that with medical care. On average, compared to other countries, we suck. There’s no polite way to put it. We die early, we’re unhealthier while we live, and our system of allocating medical care kills thousands of infants every year. Plus, we spend more than anyone. But that’s not how it is usually described (at least, not until recently, not until some of the larger businesses realized that medical costs were eating them alive). Instead, the issue is always discussed from the point of view of someone who has insurance — who has a doctor, who has “choice” (oh really?), who doesn’t want to “wait” for medical care. Not the average case, no, the special case. This is not just a con, this is an immoral con. You have great medical care, but the poor…. Of course, you’re not even getting a good price for your soul — what makes you think you are actually getting good medical care, compared to people in places you’ve never been? Who says so, and how much money are they making from the status quo?

If you stop for a moment and consider the two distributions, you realize how backwards these two uses of the average are. There’s a tremendous spread in incomes; very many people make less than $60,000, plus or minus $40,000, and a percent, or a few fractions of a percent, make 10, 100, or even a 1000 times that. On the other hand, if you consider expected lifetime, very many people live 60 years, plus or minus 40, and a very tiny set of people lives to 110. Nobody at all lives 10x the norm. So the statistic with the more normal distribution, where the average would be appropriate, we are encouraged to ignore the average, and the statistic with the funny distribution, we are expected to embrace the average.

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