Gaussian Curve: Why It Fails to Explain the Real World

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What is a Gaussian curve? In which situations can it accurately describe the world? Where does it fail, and what are its limits?

The Gaussian curve is another name for the classic bell curve, or normal distribution curve. It’s named after German mathematician Carl Friedrich Gauss, and it describes many phenomena accurately.

We’ll look at where the Gaussian curve is accurate and where (and why) it fails.

The Limits of the Gaussian Curve 

The classic bell curve—which is also called the normal distribution curve, “Gaussian distribution,” or Gaussian curve, after German mathematician Carl Friedrich Gauss—is an accurate description of Mediocristan phenomena, but it is dangerously misleading when it comes to Extremistan.

Consider human height, an eminently Mediocristan phenomenon. With every increase or decrease in height relative to the average, the odds of a person being that tall or short decline. For example, the odds that a person (man or woman) is three inches taller than the average is 1 in 6.3; 7 inches taller, 1 in 44; 11 inches taller, 1 in 740; 14 inches taller, 1 in 32,000.

It’s important to note that the odds not only decline as the height number gets further and further away from the average, but they decline at an accelerating rate. For example, the odds of someone being 7’1” are 1 in 3.5 million, but the odds of someone being just four inches taller are 1 in 1 billion, and the odds of someone being four inches taller than that are 1 in 780 billion! Human height is accurately described by the Gaussian curve (normal distribution curve).

Now consider an Extremistan phenomenon like wealth. In Europe, the probability that someone has a net worth higher than 1 million euros is 1 in 62.5; higher than 2 million euros, 1 in 250; higher than 4 million, 1 in 1,000; higher than 8 million, 1 in 4,000; and higher than 16 million, 1 in 16,000. The odds decrease at a constant, rather than accelerating, rate, indicating that their distribution doesn’t conform to a Gaussian curve.

(Note: The European wealth statistics cited above aren’t precise, but they illustrate the central point: that wealth is scalable and does not look like a bell or Gaussian curve.)

The upshot is that in Extremistan, as the name suggests, extreme events have much better odds of occurring than in Mediocristan. Simply put, the Gaussian curve does not apply.

The Mistakes of Adolphe Quételet

Adolphe Quételet (1796–1874) was a French mathematician who developed the idea of the “average human” (l’homme moyen) through the use of “means”—golden averages that represented the ideal human form.

At first, his inquiries were limited to human beings’ physical characteristics—height, weight, newborn weight, chest size—but before long, he began to seek averages in the social realm by studying human habits and morals. Quételet developed bell curves, or Gaussian curves, to describe humans’ deviance—literally—from both physical and moral norms.

Gaussian Curve: Why It Fails to Explain the Real World

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Amanda Penn

Amanda Penn is a writer and reading specialist. She’s published dozens of articles and book reviews spanning a wide range of topics, including health, relationships, psychology, science, and much more. Amanda was a Fulbright Scholar and has taught in schools in the US and South Africa. Amanda received her Master's Degree in Education from the University of Pennsylvania.

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