When Does the Average Person Not Actually Resemble Anyone in the Group?

The more characteristics you average together, the less likely any actual person is to match the result.

The average person disappears when separate averages are combined into a single person.

Average height can describe a population. So can average chest circumference, sleeve length, income, age, or spending. But combine enough of those averages and you create a statistical profile that nobody in the group possesses.

Gilbert S. Daniels demonstrated this in 1952 with 4,063 members of U.S. Air Force flying personnel.

He went looking for the “average man.”

He couldn't find one.

What happened to the average man?

Daniels began with body measurements collected in the Air Force's 1950 anthropometric survey. From the available measurements, he selected ten dimensions useful in clothing design and asked how many men were approximately average on all ten.

He was generous about what counted as average.

Instead of requiring someone to land exactly on the mathematical mean, Daniels defined an “approximately average” range around it. His method used about three-tenths of a standard deviation on either side of the mean, producing a range containing roughly the middle 25 to 30 percent of the population for an individual measurement.

Then he started eliminating people.

Of the 4,063 men, 1,055 were approximately average in stature.

Of those, 302 were also approximately average in chest circumference.

Add sleeve length and 143 remained.

After the tenth measurement: zero.

Not one of the 4,063 men fell within Daniels's average range on all ten dimensions.

Nothing was wrong with the averages. Each one accurately summarized a characteristic of the population.

The mistake was assuming they belonged to the same person.

An average becomes stranger as you make it more complete

This is the counterintuitive part.

Adding more averages feels as though it should produce a more accurate description of a person.

It produces a more detailed description of the population.

Those are different things.

Suppose you know the average customer's age. That tells you something about the customers collectively. Add average income, household size, annual spending, number of purchases, education, commute, and hours spent online, and your customer profile begins to look remarkably specific.

But you have not necessarily moved closer to an actual customer.

You have assembled the center of several different distributions into one composite.

Daniels described the problem plainly. The “average man,” he wrote, becomes especially misleading when more than one dimension is considered. His data showed why: a person near the center on one measurement moves away from the center on another.

The statistical portrait gets sharper while the human resemblance gets weaker.

There is more than one way an average can mislead

Daniels exposed a multidimensional problem: individual averages do not automatically coexist in an individual.

Other distributions break the idea of an “average person” differently.

A strongly skewed income distribution can pull the mean far above what most people earn. Two distinct populations can produce a mean located between the groups. In both cases, the arithmetic is correct while the mental picture created by the arithmetic is wrong.

These problems should not be collapsed into one.

With skew, the question is whether the mean represents the center people actually experience.

With distinct groups, the question is whether one center should describe both populations.

With Daniels's problem, the question is whether averages from different dimensions belong together at all.

That last problem is easy to miss because every number can be individually sensible.

When does this matter?

It matters when the average stops being descriptive and starts becoming a specification.

Knowing average height can help describe a population. Designing something to fit a person of average height, average arm length, average shoulder width, average leg length, and average reach assumes those dimensions occur together.

Daniels warned designers against exactly this mistake. His paper argued that human-dimensional data should be used as ranges rather than collapsed into a mythical average individual. He noted that the problem becomes more severe as a design requires more dimensions simultaneously.

The same distinction applies far beyond physical design.

An average employee, customer, student, voter, or household is useful as a statistical abstraction. Trouble starts when we expect an individual to resemble that abstraction across many characteristics at once.

So before designing for “the average person,” ask a different question:

How many actual people look like the average we just created?

Daniels asked.

Out of 4,063, the answer was zero.

📚Bookmarked for You

The End of Average by Todd Rose. Examines how systems built around averages fail to account for real human variation, including the Air Force research.

Probably Overthinking It by Allen B. Downey. Uses statistical reasoning to explain why intuitively convincing interpretations of data can be misleading.

🧬 QuestionStrings to Practice

Testing whether an average is representative.

Use this sequence when a decision relies on a statistical description of people.

What exactly are we averaging? → How widely do people differ on that measurement? → Are there distinct groups hidden inside the population? → How many characteristics must apply to the same individual? → Would a different measure or design change our decision?

One question a day. Another opportunity to think differently. Explore QuestionClass's Question-a-Day.

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