Signed Deviation Ledger Cross-Scan - Statistical Physics: Ensembles, Weights, and Fluctuations Step by Step

Variance starts with signed distances from the mean, not with a black-box square. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Deviation row 1

Value 0 minus mean 2 gives signed deviation -2.

x-\mu=0\mathbin{-}2=-2

Deviation row 2

Value 2 minus mean 2 gives signed deviation 0.

x-\mu=2\mathbin{-}2=0

Deviation row 3

Value 4 minus mean 2 gives signed deviation 2.

x-\mu=4\mathbin{-}2=2

Signs disappear only after the squaring step

The three signed deviations are negative two, zero, and positive two. This page keeps the sign visible before variance squares it.

\begin{array}{c|c|c}x&\mu&x-\mu\\0&2&-2\\2&2&0\\4&2&2\\\end{array}