Bad Math

Stephen Markacs
3 min readAug 3, 2018

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I get bothered by bad math in political posts, and have seen a couple of cases lately that really bothered me. There was this:

Its usually better to use median, not average, and if the math here wasn’t broken, this wouldn’t be an exception, but the real issue is with comparing average/median costs with minimum incomes. Why would you do that and think the result means anything? All it really means is that the income distribution curve isn’t flat. What it doesn’t say anything about is people’s ability to afford housing, because its comparing the wrong things.

You could indeed compare median incomes with median rents, and get a meaningful result. Median incomes in the US are something like $55k per household. Median rents are likely a bit less than average rents, so if the above is correct at all, maybe $1100 per month. In this case, the standard formula of income greater than 4 times rent works out. So if you are trying to make the point they want to make here, medians won’t work.

Minimum wage done full time and minimal apartment rents are less likely to work out, and could come closer to making their point… Minimum wage full time being able to afford rent at the 4 times rule would require a rent of around or less than $300 a month. I would guess that is hard to find, even in the middle of nowhere, but its nowhere near as far off as the nonsensical result they got. I wonder if they just cheated and thought it was ok (its not) or if they really didn’t realize?

Realistically, their post is just a really obtuse way to sort of say that the average income is 4 times the minimum. That seems reasonable to me, nothing to generate outrage over. What seems reasonable to you, as say the ratio between a career tradesman/serviceman and a teenager asking if you want fries with that?

And… then there was this:

beware the stray factor of population in the denominator

It may be harder to see why this is nonsense, but its actually even more broken than the first. If you take a ratio of a per person value to a per nation value, then you should expect the result to be inverse to population, which is what they are showing here. (curr pops: 6, 36, 326) The result here thus does not have any of the meaning that they act like it does. It certainly has nothing to do with trickle down economics. It just means that with a bigger pie, you get a smaller fraction of the pie.

Another way to think of it is this. If you are a nation of one, and you have a thousand dollars, you have a thousand dollars per thousand dollars of the nation’s wealth. If your friend has a thousand dollars too, and you make a nation of two, then you have 500 dollars per thousand dollars of the nations wealth. You still have the same amount of money and you are equal with your friend.

Here’s what we get if we multiply by population to remove the nonsensical stray population factor:

This fraction is something like the middle class’s share of the overall wealth… more precisely i think its the ratio between the amount of wealth there is and the amount of wealth there would be if everyone had as much wealth as the “middle class citizen”. (I wish they’d measured and said “median income” here, but…) This fraction sort of does say something.

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