Fluctuations and Balance

Variance Is a Squared-Deviation Ledger

A fluctuation label is computed from mean-centered deviations. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Variance starts after the mean is fixed

The checked mean is two.

xˉ=2\bar x=2
Fluctuation meanSquared deviations are tied to this mean.values=0,2,4weights=1,2,1mean=2squaredDeviations=4,0,4varianceNumerator=8variance=2

Variance is a squared-deviation ledger

The variance numerator is eight and the total weight is four.

σ2=84=2\sigma^{2}=\frac{8}{4}=2
Variance ledgerCaller-supplied squared deviations are rejected.values=0,2,4weights=1,2,1mean=2squaredDeviations=4,0,4varianceNumerator=8variance=2