Relation Cross-Scans

Sample Mean-Range Cross-Scan

Hold the sample mean fixed and watch the spread change. Each toy row has four samples summing to 20, so the mean stays 5 while the range grows across rows; real measurements also depend on calibration, sampling window, baseline drift, noise, and uncertainty.

A fixed average is scanned against finite sample range. 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 average can stay fixed while spread changes

The source ledger has four samples. Its average label is computed from the same checked sum and count as the range labels.

Vˉ=204=5 V\bar V=\frac{20}{4}=5\ \text{V}
Mean and range sourceAverage and range are both checked from the sample list.rawSamples=0,5,5,10 Vbaseline=0 Vsamples=0,5,5,10 Vcount=4sum=20 Vaverage=5 Vmin=0 Vmax=10 V

Same mean does not mean same spread

All three rows sum to twenty over four samples. The mean stays five, while the range grows across the rows.

samplesVˉrange(2,4,6,8)56(1,5,5,9)58(0,5,5,10)510\begin{array}{c|c|c}\text{samples}&\bar V&\text{range}\\\left(2,4,6,8\right)&5&6\\\left(1,5,5,9\right)&5&8\\\left(0,5,5,10\right)&5&10\\\end{array}
Mean-held spread scanThe final row is the checked source diagram.rawSamples=0,5,5,10 Vbaseline=0 Vsamples=0,5,5,10 Vcount=4sum=20 Vaverage=5 Vmin=0 Vmax=10 V