The Cairn

Describe the pile of data you already hold. Pick a formula, walk the four steps, watch each move build.

First principle. The Cairn works on a sample you already gathered — a finished pile of numbers. It never forecasts; it describes. Every formula here is one of three questions about that pile: where is its center, how wide is its spread, and do two columns move together. The split that runs through the whole course: the Cairn counts real stones and divides by n (or n−1); the Weighing Table weighs a distribution of what could happen by P(x). Same skeleton, different fuel.

The Line

Walk the four steps. Drop the data in Step 3 to resolve the pile.

Formula Reference — Kap 1

Mean X̄Center

X̄ = (1/n) · Σ xᵢ

Weighted mean X̄ᵥCenter

X̄ᵥ = Σ(xᵢ·wᵢ) / Σ wᵢ

Median & QuartilesCenter

median pos = (n+1)/2 · Q1 = (n+1)/4 · Q3 = 3(n+1)/4 · IQR = Q3−Q1

Sample variance Sₓ²Spread

Sₓ² = (1/(n−1)) · Σ (xᵢ − X̄)²

Population variance S² & bridgeSpread

S² = (1/n) · Σ (xᵢ − X̄)² · S = √((n−1)/n) · Sₓ

Standard deviation SₓSpread

Sₓ = √(Sₓ²)

Sample covariance SₓᵧPairs

Sₓᵧ = (1/(n−1)) · Σ (xᵢ − X̄)(yᵢ − Ȳ)

Correlation RₓᵧPairs

Rₓᵧ = Sₓᵧ / (Sₓ · Sᵧ) ∈ [−1, +1]