Averaging and Acceptance Gates

Four Readings Average to the Center

Four repeated readings form a finite measurement ledger, and the average gives the center of that stated sample. The arithmetic is exact only for the listed readings and gate rule; real measurements can include correlated noise, resolution limits, calibration drift, outliers, and sampling bias.

A repeated reading gate is an exact residual 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

Four readings average to the target

Readings 9, 11, 10, 10 volts average to 10 volts.

Vˉ=9+11+10+104=10 V\bar V=\frac{9+11+10+10}{4}=10\ \text{V}
Averaging gateThe average is checked from the finite readings.readings=9,11,10,10 Vtarget=10 Vaverage=10 Vresiduals=-1,1,0,0squaredBudget=2gateLimit=4acceptedBit=1 bit

Residuals make the acceptance finite

Against target 10 volts, residuals -1, 1, 0, 0 give squared budget 2, which is within limit 4.

(−1)2+12+02+02=2(-1)^{2}+1^{2}+0^{2}+0^{2}=2
Accepted finite runNo distribution or RMS limit is claimed.readings=9,11,10,10 Vtarget=10 Vaverage=10 Vresiduals=-1,1,0,0squaredBudget=2gateLimit=4acceptedBit=1 bit