A squared-deviation contribution cross-scan squares each state's deviation from the mean, showing how every state adds a nonnegative term to the spread. The arithmetic is exact only for the stated states, probabilities or counts, squared deviations, and rows in the ideal ensemble model. Real systems add preparation bias, finite samples, correlations, detector/counting calibration, thermalization limits, finite precision, and measurement uncertainty.
Each fluctuation term is a weight times one checked squared deviation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Squared contribution row 1
Deviation -2 squares to 4. Weight 1 makes contribution 4.
w(x−μ)2=1⋅4=4
Squared contribution row 2
Deviation 0 squares to 0. Weight 2 makes contribution 0.
w(x−μ)2=2⋅0=0
Squared contribution row 3
Deviation 2 squares to 4. Weight 1 makes contribution 4.
w(x−μ)2=1⋅4=4
The middle state has weight but zero squared deviation
Weight alone is not a fluctuation contribution. The middle row has weight two, but its deviation is zero, so its contribution is zero.