Normal Distribution

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}

The bell curve—nature's default pattern for measurements clustered around an average with spread σ.

By Abraham de Moivre, Carl Friedrich Gauss

Formal Sciences

Normal Distribution

1733 · Abraham de Moivre

Why it matters: Central to statistics, quality control, finance, and the Central Limit Theorem.

Discoverers: Abraham de Moivre, Carl Friedrich Gauss (1733)

What does it mean?

The bell curve—nature's default pattern for measurements clustered around an average with spread σ.

Central to statistics, quality control, finance, and the Central Limit Theorem.

Symbol	Name	Unit	Meaning
$μ$	Mean	—	Center of distribution
$σ$	Std deviation	—	Spread of distribution
$x$	Value	—	Random variable

Heights with μ=170cm, σ=10cm: ~68% fall between 160-180cm.

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Equation Universe

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}

Real-world impact

Global economy

Quantitative models shape markets and policy.

Photo: Unsplash — financial markets

The bell curve—nature's default pattern for measurements clustered around an average with spread σ.

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