Variance is the probability-weighted average of squared deviations from the mean, var = sum of p_i * (x_i - mean)^2, the ledger that sizes how spread out a distribution is. The arithmetic is exact only for the stated probabilities, values, and mean in the ideal ensemble model. Real systems add finite samples, preparation bias, correlations, non-equilibrium effects, rate-estimation error, and measurement uncertainty.
A fluctuation label is computed from mean-centered deviations. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Variance starts after the mean is fixed
The checked mean is two.
xˉ=2
Variance is a squared-deviation ledger
The variance numerator is eight and the total weight is four.