Estimation · three-point PERT
An estimate is a range, not a number.
Break the work down, give each task an optimistic, likely, and pessimistic figure, and this rolls the whole thing up — expected duration and cost, with the confidence interval around them. Deviations combine in quadrature, which is the part most spreadsheets get wrong.
E = (O + 4M + P) ÷ 6
σ = (P − O) ÷ 6
σ total = √(Σσ²)
The band is the confidence interval. The ticks are the absolute best and worst case — every task at its optimistic figure, then every task at its pessimistic one.
Work breakdown
Optimistic · most likely · pessimistic, per taskRolled-up deviation assumes tasks vary independently. Where the same risk drives several tasks — one vendor, one scarce specialist, one permit — the real spread is wider than this shows. Treat the band as a floor on your uncertainty, not a ceiling.