The single-spike scan keeps the sample count fixed while one top sample moves. With top sample 8, the average is 5 and the range is 6; raising that one sample to 12 raises the average to 6 and widens the ledger. Real spike handling needs sensor checks, saturation limits, filtering choices, repeated records, and uncertainty before deciding whether an outlier is signal or noise.
One changing sample moves both mean and range in a finite ledger. 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 first row is a balanced four-sample ledger
With top sample eight, the average is five and the range is six.
Vˉ=5,R=6
Raising one sample moves both average and range
Changing only the top sample to twelve raises the average to six.
Vˉ=6,R=10
A larger spike keeps the count but widens the ledger
The third row shows why one outlier changes more than a caption.