The Republican Tax Reform: Part 10—Average/Mean vs. Median Outcomes

Here’s something to watch out for (in the sense that it’s a hazard you need be aware of).

It’s a very common technique when trying to justify positions going towards both ends of the political spectrum to be selective about using the mean and median.

Typically this takes the form of citing a mean and then comparing it to a median. Casual readers and the innumerate can get fooled by this.

First, a little statistics review. One of the first things taught in statistics is to determine whether the data are (roughly) symmetrical or not. This is usually discussed before the calculation of simple statistics. After that, you’re introduced to measure of central location of data distributions: the mean (average), median, and mode(s).

You all know how to calculate a mean: sum the values, and divide by the number of observations.

The median sounds easier, but ends up being more work: rank the observations from smallest to largest, and find the one that’s in the middle so that half are larger and half are smaller.

One of the reasons we have more than one measure is asymmetry. If your data is symmetric, the mean and median are the same. If it is asymmetric, it’s very likely that they are different.

For example, if my distribution contains the observations 1, 2, and 3, the mean is 2, and so it the median. But if my distribution contains the observations 1, 2, and 9, the mean is now 4, but the median is still 2.

This comes up a lot in macroeconomics (and finance) because of the prevalence of variables that begin as counts of stuff. Counts start at zero, so they’ve got a solid end on the lower end of the distribution. But they don’t often have limits at the top end, so the tail on that side of the distribution can be much longer. This tends to make the mean (average) larger than the median.

For example, things like income and home prices have distributions that are asymmetrical in this way. What this means is that someone of average income can afford the median home, but someone of median income can’t afford the average home. Often you see something like the latter case being used as the basis for outrage in the legacy media. But do not that both of those can be true, and in the same situation it can still be true that someone of average income can afford the average home, and someone of median income can afford the median home.

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So how are Republicans and Democrats going to spin this?

Watch out if Republicans say the average tax payer will have their taxes go down. That can be code for taxes were reduced on the top end of the distribution.

Watch out if the Democrats say the median taxpayer is largely unaffected by this reform. In the U.S., the median taxpayer pays close to nothing as it is, so it’s hard to reduce that.

But what if both of those are kinda’ sorta’ correct? Data on this is not easy to come by, but you should focus on stories about households making around, say, $100K per year (which is around the 80th percentile). This is close enough to the top that they’re paying a lot of taxes, yet close enough to the middle that a cut could seriously improve their lives.