Paired Average Keeps the Difference - Signals and Noise in Physics Measurements Step by Step

Paired averages keep two channel ledgers separate before subtracting their centers, so common processing does not erase the stated difference. The difference is exact only for the listed samples and pairing rule; real comparisons need uncertainty budgets for offset, gain, timing, noise correlation, and sampling bias.

Two finite averages can be subtracted without claiming population statistics. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Each channel gets its own average

Channel A average is 7 volts and channel B average is 3 volts.

\bar A=7\ \text{V},\quad \bar B=3\ \text{V}

The paired difference is finite subtraction

The measured difference is 7 minus 3, giving 4 volts.

7+(-3)=4\ \text{V}