We Are All Average

The Grand Average Hypothesis

People have many different characteristics. With so many characteristics and so many people, it's not unreasonable that a given person is exceptional in one regard or another. However, by that same token, as you tally up measures you are likely to find that all of us are 'average' in a very real sense. 

This exposition outlines the Grand Average Hypothesis, a conceptual framework that explains why individuals who feel "unusual" in one specific trait are statistically likely to be average when their entire profile is considered.

This redo utilizes verified statistical principles and references the work of Adolphe Quetelet and Todd Rose, whose research directly addresses the "science of the average" (Quetelet, 1835; Rose, 2016).

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The Grand Average Hypothesis: A Statistical Defense of Normality

While we often define ourselves by a single "jagged" trait—such as being exceptionally tall or struggling with a specific skill—statistical laws suggest that these deviations are outliers in a much larger, remarkably average system.

1. The Individual as a Sample of Infinite Traits

In classical statistics, the Law of Large Numbers (LLN) states that as a sample size increases, its mean converges toward the population average (Lakehead University, 2024). While typically applied to groups of people, this hypothesis treats a single person as a "sample" of K different characteristics.

If we standardize every measurable human characteristic (bone density, reaction time, T-cell count, musical pitch discrimination, etc.) into Z-scores—where the population mean is 0 -- then any individual is a collection of K scores.

2. The Central Limit Theorem and "The Average Man"

The Central Limit Theorem (CLT) states that the sum or average of a large number of independent variables tends toward a normal distribution (NIH PMC, 2017).

• Historical Context: Adolphe Quetelet, the father of anthropometry, proposed the concept of l'homme moyen (the "average man"). He argued that the mean represents a "constant cause," and individual variations are merely "accidental errors" (Wikipedia, 2026; Quetelet, 1835).

• The Statistical "Wash": If an individual's traits T1, T2, ... TK are largely independent, their "Grand Average" score (Si) becomes increasingly stable as more traits are measured.

• The Shrinking Deviation: The variability of an aggregate profile is governed by the formula: 

  
  
  
  As K (the number of traits) grows, the standard deviation of your "total self" shrinks toward zero. This means that while you may be 3σ (an extreme outlier) in height, that deviation is diluted by the thousands of other traits where you are likely closer to the mean.

3. The Challenge of "Jaggedness"

Modern critics like Todd Rose argue that "the average person" is a myth because human traits are jagged—they are not perfectly correlated (Rose, 2016). For example, a person with high "g-factor" (general intelligence) might still have poor spatial reasoning.

However, from the perspective of the Grand Average Hypothesis, this jaggedness is exactly what guarantees "averageness" in the aggregate. Because our strengths and weaknesses do not move in perfect lockstep, they statistically "cancel out" when viewed as a whole system.

Trait Type	Examples	Statistical Behavior
Independent Traits	Eye color, finger length, reaction speed	Strongest pull toward the aggregate mean.
Correlated Clusters	Cognitive abilities, physical fitness	Resist the mean locally, but diluted globally.
The "Total Self"	The sum of all $K$ traits	Statistically certain to be "Average."

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Conclusion: A Statistical Balm

The value of this hypothesis is its ability to attenuate the weight of exceptionalism. It reminds us that a single departure from the norm does not define a person’s total standing. In the grand tally of human measurement, the "noise" of one exceptional trait is drowned out by the "signal" of our collective humanity.

References and Further Reading

• Adolphe Quetelet (1835): A Treatise on Man and the Development of His Faculties. Read more on Wikipedia.

• Todd Rose (2016): The End of Average. Summary at Blinkist.

• NIH PubMed Central (2017): Central limit theorem: the cornerstone of modern statistics. Read article.

• Lakehead University: The Law of Large Numbers and its Applications. Access PDF.