Boundary Depth Scans

Baseline Offset Average Three-Row Scan

Baseline subtraction shifts the sample average while preserving 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

Zero baseline leaves the raw average in place

The raw samples average to eight volts before any offset is removed.

Vˉ=8 V\bar V=8\ \text{V}
Zero-baseline sample rowRaw and net samples match when the baseline is zero.rawSamples=5,7,9,11 Vbaseline=0 Vsamples=5,7,9,11 Vcount=4sum=32 Vaverage=8 Vmin=5 Vmax=11 V

Subtracting two volts shifts the whole ledger

The same raw samples now average six volts after the baseline shift.

8−2=68\mathbin{-}2=6
Two-volt baseline rowEvery net sample is checked against raw minus baseline.rawSamples=5,7,9,11 Vbaseline=2 Vsamples=3,5,7,9 Vcount=4sum=24 Vaverage=6 Vmin=3 Vmax=9 V

The range stays fixed while the baseline moves the mean

All rows use the same raw samples. Baseline changes the average, but not the spread between min and max.

baseVˉrange086266446\begin{array}{c|c|c}\text{base}&\bar V&\text{range}\\0&8&6\\2&6&6\\4&4&6\\\end{array}
Four-volt baseline rowThe offset source is visible in the sample ledger.rawSamples=5,7,9,11 Vbaseline=4 Vsamples=1,3,5,7 Vcount=4sum=16 Vaverage=4 Vmin=1 Vmax=7 V