Planet Money and the New York Times’ Ben Casselman teamed up to try to demonstrate that, “Mode, not average, is a better way to find the typical American.” They are wrong.

Here is how they set up the issue:

MALONE: My issue is with this thing that people talk about, the average American. …Who is average, really? …I think people don’t mean average American. I think what they actually mean is, who is the person – if I walk outside into America, who is the person I’m most likely to run into?

JACOB GOLDSTEIN: Yes, the person who there’s more of that person than any other person.

MALONE: That ain’t the average. It’s not the median… If you actually want to figure out what human beings exist outside your door, you need to run the mode.

Instead of demonstrating how useful the mode is, they actually do a pretty good job of demonstrating why nobody uses it: it sucks for most uses.

What is the mode? It is simply the most common value in a set of data. For example, suppose you have a room with seven people and their annual incomes are:

$1,000; $1,000; $30,0000; $40,000; $50,000; $60,000; and $100 million

The modal income is $1,000 because there are two people with that income and only one person at every other number. The median is the most useful statistic for understanding the central tendency of this group’s income because it is the value in the middle, $40,000, which is the most central value. The mean is $14.4 million which is much closer to the one rich outlier than to anyone else, so it is also a poor measure of central tendency for the group.

The median does the best here because it is the least sensitive to outliers. If another person with $100 million walks into the room, then the mean would nearly double, and the mode would be both $100 million and $1,000. Both of those statistics are unrepresentative whereas the median would still be near the center of the numbers and hardly affected at all.

The mode is only the best measure for categorical data like color. For example, if we have seven colors:

red, red, orange, yellow, green, blue, ultraviolet

In this case, it is impossible to take the mean and if we don’t care about the order of the colors, then we cannot take the median either so the mode (red) is the best measure of central tendency simply because none of the better options are impossible. The best you can do is say that red is the most common color and that is the same thing as saying that red is the modal color.

But for quantitative data we can calculate the mean or median and the mode is rarely as useful as either of them. Planet Money demonstrated how ridiculous the mode is for numerical data when they claimed that the modal income is $30,000 to $75,000. That is a misunderstanding of what a mode is! The range of their so-called mode is so large, it is laughable. It ranges from $30,000 which is about the poverty line for a family of five up to $75,000 which would be the the upper-middle class for a single individual. Nearly a third of US households (29%) are in what NPR calls their “modal” range.

Why did they pick such a huge range? Well, perhaps there are a very similar number of households that earn between $30,000 and $75,000 so they might have been uncertain about what the true mode is. There is always some uncertainty in data collection because measurements aren’t always perfect. For example, if a household says they earn $30,000, they might be a little off and they might actually earn $31,000 or $29,000, so the real number could be plus or minus a thousand or more. Given modest uncertainty in the data, there is usually a large range in the possible true value of the mode and perhaps in this case the NPR authors could not give any more precision than that the true modal values must be somewhere between $30,000 and $75.000!

The median income is much easier to pin down. In this case we would just find the observation in the middle, which was about $63,000 in 2018, and if there is uncertainty of plus or minus $1,000 then we would know that the true median is between $62,000 and $64,000. That is much more precise and useful.

*UPDATE: In their methodology description, Planet Money explains that they just arbitrarily lumped households into four income groups. This is even worse than I had originally thought. With this methodology, it would be possible to say that the modal income is nearly anything. For example, I could say that the modal income is between $1 million and $1 billion simply by splitting up all the lower-income categories into smaller buckets. *

Planet Money’s search for the modal American gets even more bizarre after that. They determine that, “The modal American, based on our criteria, is in fact, a child.” But then because they really wanted the modal American to be an adult, they abandoned the mode and just changed their criteria to get an adult which was what they had originally wanted all along.

So after abandoning the mode for determining age, they just looked at adult Americans and then they arbitrarily only the adults divided into ethnic buckets according to ethnic categories which happened to clump people from Portugal, Ireland, Russia, and many from Latin America into the “white” category so that they could claim the “white” identity as being “central” to “average” America.

Then they arbitrarily decided that they did not really want all adults because they had a preconceived notion that Gen X is more “central” to America even though Gen X is far from the true mode. There are both more Baby Boomers and more “echo boomers” (millennials) than members of Gen X, but they didn’t really care about the mode and wanted someone who is “middle age” which would be the median age (38). They lamented that this is “one of the least common ages” and instead of staying with the modal age (26), they just switched their criteria again and picked someone from Gen X.

In the end, they seemed to arbitrarily pick what they had probably had as their preconceived notion of the average American. Someone who is:

- Gen X (even though the modal American is age 26)
- “upper-middle-class income. The household income is between $75,000 and $165,000 a year. ” (Even though this is way higher than either the modal income or the median income and is closer to mean household income.)
- married (Even though the modal American is unmarried)
- male (Although they admit that the modal American is female, they only interview men and repeatedly talk about how they are looking for the “average guy”. They never really wanted the modal American because they are so lazer focused on the “homogeneous experience” of, ” white, Gen X
“)*men* - employed (Even though there are more Americans without a job than with a job)
- no college degree (this is a vast range of schooling from zero years to sixteen plus (including about a fourth of Americans who take some college classes without getting a 4-year college degree). About 2/3 of Americans have less than a college degree, so it is not really the modal amount of education because it is so unspecific.)
- lives in the suburbs
- white
- wears plaid shirts! (I think this was an attempt at a joke.)

I only have minor quibbles with white and suburban, but other than that, they completely ignored the modal value for most of their criteria. If I didn’t know better, I’d think Planet Money started out with a picture of the kind of guy that they consider to be the most essentially American and then picked arbitrary categories and tortured the statistics until they got what they wanted.

This ‘analysis’ is a good demonstration why almost nobody uses the mode. Even when Planet Money tried to use it, they couldn’t stick with it because it didn’t give them the results that they were looking for and so they just kept changing their rules until they got… demographics that look like something pretty close to the median Trump supporter. You know, “real Americans“.

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