Compute variance without retaining every observation — Another Way Through

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Goal: obtain population variance from a stream without storing all n values. Initialize n=0, mean=0 and M2=0. For each x, increment n; set delta=x-mean; update mean += delta/n; then M2 += delta*(x-mean). Return M2/n for n>0 (or M2/(n-1) for sample variance when n>1). For [2,4,4], states (n,mean,M2) are (1,2,0), (2,3,2), (3,10/3,8/3); population variance is 8/9. This route keeps constant state and preserves the variance objective. It does not retain the original records or supply an exact median. Floating-point rounding remains relevant; the formulas are exact over real arithmetic.

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