How typical is a median person?

I have talked about cautions and implicit assumptions that surface around the use of averages before, but seeing a few references to the “median person” in the news a couple of weeks ago led me to writing this post for the Statisticians React to the News blog. I am cross-posting it here.

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Last week, references to a “median person” showed up enough times in my life to spur me to write this post.  I think the use of an “average person” is still more popular, but this “median person” seems to be gaining popularity too.  Regardless, as attached to a person, the concept is essentially the same – it’s an appealing way to take a collection of averages (or medians) calculated for each of many measured characteristics and conceptually construct a new individual, as least hypothetically. The question that doesn’t get asked enough — Who, if anyone, does an individual constructed in this way actually “look” like? 

There’s certainly an appeal to the phrase, most obviously that it is short (in number of words), but there’s also something story-like and personal conveyed that makes it easy to digest.  Would you rather read “the median voter is expected to …” or something like “we predict a person with median income, median socio-economic status, in a median sized county, of median age will vote …”   It’s easy to see why journalists, and researchers, use the shortcut. The median voter description actually conjures up an image of a particular type of person, mostly likely a “typical” person – which of course probably looks different to each of us based on our own biases and experiences of what is typical.  Sometimes writers will provide a description, but usually it’s up to us as readers to throw a little reality check into our thinking – to ask about how the median/average person is defined and how useful the hypothetical individual really is.

The main problem comes from the natural, though potentially misleading, connection between the concepts of a median/average person and a “typical” or “common” person. Journalists may never explicitly say they are talking about a typical or common person, but there is a tendency for our brains to go there. The extent of the problem largely depends on how many characteristics are being used to construct the hypothetical person. If we’re only defining an average or median person based off one characteristic, then it can be perfectly reasonable, as long as there are many individuals in the group of interest who do fall near the average or median.  But, imagine when the list of characteristics defining the person starts to get long!  The median person is defined as an individual whose measurements of all the characteristics of interest are at, or very close to, the median!  As the list of characteristics gets longer, the median or average person becomes rarer and rarer — such that the hypothetical person described is not at all typical or common, and might not even exist!

The story of the average pilot

Todd Rose, in his book The End of Average, uses an effective historical example to illustrate this point.  In the 1940’s, the United States Air Force was experiencing an issue with too many pilots losing control of their planes, which ultimately led to examining the design of the cockpits. It’s hard to imagine now, but the first cockpits were fixed in their dimensions with no way to adjust things like the shape of the seat, the distance to the pedals and stick, the height of windshield, etc.  To get the fixed dimensions used in all planes, the engineers took measurements of physical dimensions of 100’s of male pilots in 1926, calculated the averages, assumed the collection of them represented an average pilot, and then designed the cockpit according to the those dimensions.

Decades later, when the cockpit dimensions became a suspect in the rate of crashes, the initial thought was that the size of the average pilot had just changed. They decided to update their average pilot dimensions with a more data – measuring 140 dimensions on over 4000 pilots!  Fortuitously, they hired a physical anthropologist, Gilbert Daniels, to participate in collecting and analyzing the data. Daniels had just finished graduate work in anthropology where he had measured dimensions of human hands – and he had concluded that the idea of an “average hand” was not useful because the average hand, as constructed from the collection of many average dimensions, did not resemble any individual’s hand measurements.

Needless to say, Daniels’ previous work led to skepticism about the “average pilot” idea and he used the data to do a little extra analysis. Based on just 10 of the physical dimensions thought to be most relevant to cockpit size, he defined an “average pilot” as an individual with measured dimensions falling within the middle 30% of the range of values for each of the ten dimensions (a pretty loose definition!). He then went through the individual pilots to count the number who met the “average pilot” criteria. There was general agreement among Air Force researchers that most pilots would be considered “average” based on this definition – recall that pilots, at least at that time, were already pre-selected based on their size to fit into the existing cockpits!

How do you think it came out?  Well, out of the 4063 pilots, none (zero!) of the pilots met the “average pilot” criteria!  Even for just three relevant characteristics, less than 3.5 percent had all three measurements fall near enough to the individual dimension averages.   The “average pilot” just didn’t exist – the cockpit had been designed to fit no-one!  This ultimately led to cockpits with adjustable features, and of course eventually to all the ergonomic adjustments we have in our cars, and even bikes, today.  Can you imagine trying to drive a car made just for the average person?

As an aside, there is a lot of interesting history (and far reaching implications!) related to going after the concept of an average person – starting in the mid-1800’s with the work of a Belgian astronomer turned social scientist, Adolph Quetelet. The End of Average provides a nice starting place for those interested.

How big is the problem?

Is this a big problem in reading the news? It depends. How long is the list of characteristics? Do many characteristics tend to vary together, or do individual profiles (collections of measurements) tend to look very different?  Do we attach too much meaning to an “median person” and can we get beyond the “typical” and “common” misinterpretation?  The distinction can seem subtle between a “median person” and a “hypothetical person with all characteristics falling at median values,” but the implications in terms of what one takes away from the article may not be subtle. It’s so tempting to assume the “median person” looks close to us or the people we know.

The phrase also gives writers the easy chance to leave out the list of characteristics used in the definition, which takes away a chance for readers to have information that could be used to better criticize the work or consider how it might apply to them or those people they care about.  We are usually in need of more details about what’s behind a stated result – and cute, vague shortcuts don’t do us any favors in such a situation, except to reduce the number of words we must read.

The “real median voter”

Some writers at least acknowledge the issue; this very short section called “The real median voter” showed up in the New York Times The Morning newsletter on September 29, 2021 by David Leonhardt and Ian Prasad Philbrick. The authors discuss the assumption made by those in elite U.S. political circles that a “median voter” is a “political moderate” (that happens to look a lot like those around them), and contrast that with what is actually common in the rest of the country where “this ideological combination is not so common.”  From a political perspective, the essay has some shortcomings, but I was still happy to see some explicit acknowledgment of problems with the interpretation of a “median person” — that the median person is probably not common, and that our ideas of what a median person may look like depend on who we are surrounded by.

In summary

I hope more journalists, and readers, can do a better job asking how typical or common a median or average person might really be in a particular situation. It is worth trying to separate our image of an actual person from the more appropriate, but also more boring, idea of simply reporting some prediction based on average or median values of all the characteristics, or variables, of interest – even if a person with that combination of characteristics does not exist.