Fluctuation Depth Scans

Variance Numerator Quotient Scan

The variance quotient is the weighted squared-deviation numerator over total weight. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The numerator is the sum of weighted squared terms

The three contributions are 4, 0, and 4. Their sum is 8.

Nσ=4+0+4=8N_{\sigma}=4+0+4=8
Variance numeratorThe numerator is assembled from the contribution rows.xwdsqterm01-24422000412444 + 0 + 4 gives numerator 8

The denominator is total weight

The weights are 1, 2, and 1. Their total is 4.

W=1+2+1=4W=1+2+1=4
Variance denominatorThe denominator is the same weight ledger.xwdsqterm01-24422000412441 + 2 + 1 gives total weight 4

Variance is numerator over total weight

Variance divides numerator 8 by total weight 4, giving 2.

σ2=84=2\sigma^{2}=\frac{8}{4}=2
Variance quotientThe checked fluctuation ledger pins the quotient.xwdsqterm01-24422000412448 over 4 gives variance 2