Commentary: What's Wrong with Average?

Updated: Oct 13

Your life, your dreams, and your goals are not average. To you and your family they are the most eminent goals in existence. Our job is to help you make decisions that are calculated and mathematical when it is useful, and to interject common sense into the situation when mathematics will not do.

Large and small man, both wearing average size clothing that does not fit
“A horse that can count to ten is a remarkable horse, not a remarkable mathematician.” -Samuel Johnson

Dear Family, Friends, and Clients:

On September 18, 1947, The United States Air Force was designated as a separate branch of the United States Armed Forces as part National Security Act of 1947. Previously, the branch was known as the United States Army Air Forces and was a subdivision of the U.S. Army. The organization had roots going back to 1907 when it was officially established as the Aeronautical Division, Signal Corps. The new leadership of the USAF encountered a serious problem within its fledging branch: US pilots could not maintain control of their aircraft and were crashing at an unexpected rate. In fact, on a single day during this period, there were 17 independent incidents or accidents logged. Almost all these events were classified as pilot error because mechanical failure was highly irregular. It was an incredible mystery why expertly trained and decorated US pilots were having so many mishaps.

After several thorough investigations could not identify obvious mechanical or training insufficiencies, USAF engineers turned their attention to cockpit design, which was based on data collected from measuring hundreds of pilots in 1926. For over 20 years, cockpit layout had been consistently tailored to fit the “average” 1926 pilot; the size of the cockpit, seat depth, windshield size, and even flight suits and helmet straps were based on these measurements. Several theories, including a large increase in pilot size, were examined with no obvious conclusions. In response, the USAF commissioned the largest study on pilot size ever attempted. In 1950, thousands of pilots were measured on 140 criteria including Stature, Chest Circumferences, Sleeve Length, Crotch Height, Hip Circumference, Thigh Circumference, and Crotch Length.

A 23-year-old Lieutenant named Gilbert Daniels was hired to help with the measurement study. Daniels had been a physical anthropology major at Harvard University, a specialty that studies the unique anatomy of the human body. As Lt. Daniels measured and compiled data on 4,063 USAF pilots at Wright Air Force Base, he started to harbor doubts that “average” was relevant when it comes to human anatomy. He examined data on the 10 most important measurements to cockpit design and found the following data, which was published in his report: The “Average Man”. In the report, he identified the following:

of the original 4063 men

  • 1055 were of approximately average stature

of these 1055 men

  • 302 were also of approximately average chest circumference

of these 302 men

  • 143 were also of approximately average sleeve length

of these 143 men

  • 73 were also of approximately average crotch height

of these 73 men

  • 28 were also of approximately average torso circumference

of these 28 men

  • 12 were also of approximately average hip circumference

of these 12 men

  • 6 were also of approximately average neck circumference

of these 6 men

  • 3 were also of approximately average waist circumference

of these 3 men

  • 2 were also of approximately average thigh circumference

of these 2 men

  • 0 were also of approximately average crotch length

His report stated:

“The tendency to think in terms of the ‘average man’ is a pitfall into which many persons blunder when attempting to apply human body size data to design problems. Actually, it is virtually impossible to find an ‘average man’ in the Air Force population. This is not because of any unique traits of this group of men, but because of the great variability of bodily dimensions which is characteristic of all men.”

Luckily, the USAF took this report seriously. They realized that the cockpit must be fit to the man, and that it is nearly impossible to fit the man to the cockpit. Against the great protests of impossibility from manufacturers- adjustable seats, levers, and flight suits were designed and incorporated into the aircraft. These are standard features that we now take for granted in our automobiles. Incidents and accidents plummeted and flying became much safer as the USAF became the greatest military air division in the world. It appears that “any system designed around the average person is doomed to fail”, but why did we focus so much on average?

The Beginnings of Average:

What does it mean to be average? Merriam-Webster says that average is “a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values”

The concept of “average” is revolutionary because it seeks to make data more useful by discarding information; namely, the individuality of each observation is ignored, and the summary statistic is used for analysis. Certain important knowledge like the mental state of the observer, or the age and accuracy of the equipment utilized, or the current relative humidity in the testing environment is ignored and assumed to cancel with equal and opposite magnitude effects of other anomalies. The first documented use of a “mean observation” was from 1635 according to The Seven Pillars of Statistical Wisdom, and was used to establish “variation of the needle” in calculating the adjustment factor needed to reconcile “true north” from “magnetic north” for documentation in navigational maps.

In 1874 Venus made transit across the face of the sun for the first time in 105 years, and astronomers worldwide were intent on calculating the precise duration of the journey. They flocked to the most advantageous locations for viewing across the globe. The intent was to utilize the time of transit to make calculations of the size of the solar system. Unfortunately, there was a wide variation in time calculated among astronomers. Differences in skill, equipment, weather, location, and time all contributed to this variance. The agreed upon solution was to take the average calculated time as the official statistic, as had been the convention in astronomy for decades.

Adolphe Quetelet (born in Belgium in 1796) was an unquestionably brilliant polymath who specialized in astronomy, mathematics, statistics, and sociology. As an astronomer he had observed first-hand the difficulty of measuring astronomical distance using eyes and stopwatches and learned the power of using averaging to standardize variant measures between astronomers that would later be used after the transit of Venus in 1874. In 1823 Quetelet convinced the Belgian government to build its first observatory and name him as the director. Unfortunately, during the Belgian Revolutionary War in 1830, the observatory was occupied by rebel forces, and Quetelet was unable to return to his position. The experience had a deep effect on a man who for most of his life had been insulated from social forces and politics and he concluded that if averaging was sufficient to measure the heavens, surely it was also sufficient for measuring humans.

Quetelet set out to build an academic discipline of Social Physics. His goal was to use mathematics to develop laws and policies that would lead to stability and prevent social disorder. In the 1840’s Quetelet analyzed a dataset that measured the chest size of 5,738 Scottish soldiers for use in constructing uniforms. He added all the observations together and divided by the number of observations and determined that the average chest size of a Scottish soldier was 39.75 inches. So what?

Quetelet set out to define the importance of this new statistic. Is it an estimate of normal? Is it what one would expect in a randomly selected individual? Some other esoteric meaning? Quetelet, having come from astronomy took the astronomer’s view of the importance of the mean. In astronomy it was assumed that all observations taken by a human observer contained some sort of error factor. The mean number was the minimization of all these errors and the true value of the measured statistic. It seems that average was the pinnacle of perfection, and that all deviations from average were errors or deformities. This opinion was corroborated by a proof completed by Carl Gauss that posited that the average was as close to the truth as possible. It seems that in Quetelet’s mind, we are all a collection of errors deviating from the divine template of design intended by our creator. Quetelet went on to establish the Body Mass Index (BMI) to allow us all to revel in our divergence from perfection.

A former pupil of Quetelet, Sir Francis Galton, was a wealthy Englishman whose family money had come from gun manufacturing and banking. While he admired Quetelet, he disagreed on one major point: average is not universal perfection, it should be improved upon at all costs. Average was synonymous with mediocre in his opinion. He stratified individuals by their relation to average into three categories: Eminent, Mediocre, and Imbecile. Further, Galton believed that one’s relation to average was universal. Eminent individuals were inherently smart, athletic, and savvy in business matters. The mediocre, were doomed to remain so in every way. To facilitate his shift from the ideal of average to the mediocrity of average, he sought to transform the definition from “error” to “rank”. An individual’s relative position to average was no longer the imperfection, it was the order in which this individual existed among his peers. Lest you scoff at the wisdom of this thinking, consider our modern usage of things like standardized tests and entrance exams in evaluating the academic potential of our children. So here we are in modern society, with Quetelet’s concept of the average man being perfect, and Galton’s idea of rank in determining an individual’s worth; one man striving to achieve average, another trying to be as far from average as possible.