There’s a common idea floating around that needs to die. It’s common enough that I have heard it several times in the last months, both in professional contexts (in the mouths of august and eloquent professors) and non-professional ones. That is the idea of the “average person.”

The idea of the “average person” takes the form of the “average public” when discussing what people think about the medieval world, “average student” when in the mouth of a professor, or the “average visitor” when it comes to the museum. In common parlance we even have snappy phrases for the idea—“**John/Joe Q. Public**”, “John Doe”, “Tom, Dick and Harry”.

Let me be quite clear. **“John Q. Public” is not real.** And even if he were, we have absolutely no reason to pay any attention to him. He is, at best, a sly cover for the speaker’s ill-informed views, and at worst, a rhetorical trick designed to reinforce the status quo and the tyranny of the majority.

Allow me to illustrate one example of what I mean.

A few months ago, I engaged in a heated discussion with a friend at a dinner party. After a few glasses of wine, the topic turned towards museums and my work at the Smithsonian. I had just lamented that many museums—particularly contemporary art museums—rarely give much meaningful context to the work on their walls. He took some issue with that.

“The average museum visitor,” he began, “isn’t really interested in reading all those little signs. They don’t want to read.”

I had to stop him.

“That’s not a thing.”

He looked confused. I repeated: “‘The average museum visitor.’—**That’s not a thing.**”

He scoffed. *Of course* there is such a thing as an average museum-goer! He then proceeded to explain, in not so many words, that the average looked, sounded, thought and felt very much like he did—only dumber.

Leaving aside the straw-guy-at-a-dinner party, this is an idea I’ve heard by colleagues in the museum field and academics, both in publications and in person. The notion that there is an average public is pervasive.

**It is also a myth.**

Here is the problem. *It is impossible to average a group of people*—at least in the way that “average” typically means. And to prove it, all we need is some pretty simple math.

*Strap in folks. It’s math time.*

Don’t worry, we’re not talking about complex statistical analyses or even linear algebra. This is all pretty basic.

There are three ways of conceiving of an “average:” the **mean, **the **median **and the **mode**. “Average”, as used in common parlance, most often refers to the **mean. **

The **mean **of any set of numbers is calculated by adding them together, then dividing that sum total by how many numbers were in the set. It is the way a GPA is most often calculated, or an Earned Run Average in baseball. It’s what happens when you call the *=AVERAGE()* function in Microsoft Excel.

Calculating the **mean**, the “average” human has slightly fewer than two arms and/or legs.

There is a sense of fairness about a mean, of equilibrium, being the exact mathematical mid-point in the data set—which may be why “average” typically refers to this.

The **median**, on the other hand is the middle point of the set. Thus, if you have a set of ten numbers from one to ten that are equally distributed (so, a set of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10), both the mean and the median would be 5.

However, if they were not evenly distributed, that is when things become interesting. Let’s say you have a set of (1, 1, 1, 1, 2, 4,8, 10, 10, and 10). The median is 2—it’s the middle number in the set. The mean would be 4.8. The median number of legs on all humans is two. ^{[citation needed]}

Medians are useful because it gives a better (though still simplistic) idea of how evenly distributed the numbers are. The **mean** household income of the USA ($72,641 in 2013) is much higher than the **median**($51,939 in 2013), because of the vast income of a few individuals at the very top [**see this table, page 29**].

**Income inequality; it’s a thing.**

The final way of understanding averages is the least common—the **mode. The mode **is the number that appears most often in the set—so in our previous set (1, 1, 1, 1, 2, 4, 8 , 10, 10, 10), the mode is 1. This is statistically useful in that it allows comparison of apples and oranges—even literally. If you have six apples and four oranges, the mode is apples. Trying to take a mean of that set can be confusing because you are comparing **qualitative data rather **than** quantitative data**.

**Quantitative data** tends to be the things people think about when they think of “data”, especially in our “big data” world. Quantitative data is data that is fundamentally countable: how many, how long, how often.

**Qualitative data**, on the other hand, is descriptive and discursive—it is textual and conceptual rather than numerical.

The fundamental problem in the old adage of comparing apples and oranges is that they are **qualitatively **different. So, if you try to take the **mean** of them, the only thing you can come up with is a weird new fruit that is somehow 60% apple and 40% orange. The median of that set seems to be simple, but isn’t: throw four lemons into the mix, and suddenly the median makes no sense because *which is the middle fruit?*

* *

# “Averaging” People

That understanding firmly in place, let’s talk about people.

People only have a few *quantifiable* properties: Age. Income. Height. Weight. Numbers of limbs. Perhaps a few others. Outweighing these basic metrics are the ways in which humans are *qualitatively* different—our social class, our race and ethnicity, our education, our sexualities, our identities, our experiences, our interests, skills, and abilities.

Of course, there are those ways in which we attempt to quantify the qualitative—IQ or SAT scores, for example, which are **notoriously problematic** as ways of **judging** such a complex concept as intelligence.

And therein lies the rub. Who then is the “average person?” Who is the “average public” or the “average museum-goer?”

Pulling numbers at random, if 27% of visitors to a museum are Latino/a, 10% Asian, 40% White and 33% African-American, then what is the “average” of that? There is no mean and no median. The only “average” left is that the **mode is White**. But saying that it is the “average” is rather deceptive. Instead of an “average”—in the common parlance meaning some kind of “fair and balanced” arithmetic mean—it simply means the dominant group. The “average” visitor, in our above group, ignores 60% of people: the majority.

That’s the problem with the concept of the “average visitor,” or the “average public”. It seeks to quantify inherently qualitative differences. As it’s used commonly, it’s a cheap rhetorical trick used by a speaker to give their ideas an imaginary person to act as a puppet. This aims to give them an air of unwarranted credibility—without actually studying who the “publics” or the “visitors” might actually be, or actually asking them what they might think. Or, more insidiously, it is used by the dominant group to claim the “naturalness” of their position. John Q. Public is, by default, male.

So, even if there were such a thing as the “average person,” why should we be particularly interested in them? Across the humanities, we are not trying to speak the same old lessons to the same people we always have, but to reach out to new audiences, to broaden the appeal of our stories, and listen to the perspectives of all those people who are not average—people like you.

Paul B. Sturtevant is Editor-in-Chief of *The Public Medievalist*. He is a researcher and historian for the Smithsonian Institution, where he helps the institution better understand its visitors and itself. He is an author, a medievalist, and a consultant, and has completed research projects as diverse as exploring the Caliphates of Muslim Spain, the history of American health care reform, and the peculiarities of American-style barbecue. He is unabashedly passionate about the place history has in current conversations.

Very interesting article. Pesky math getting in the way of our myths!