LiquidPlanner uses some moderately sophisticated statistics to calculate things like ranges of dates and ranges of remaining work for the overall project.

## Statistics for Scheduling

You can’t just add up all the best case estimates and then add up all the worst case estimates from the individual tasks in a project. Doing that would get you a range that is much larger than what it should be, realistically. If you did total up the estimates, you would be seeing the effort for if absolutely *everything* goes right/wrong.

But it is very unlikely that everything will go right (or even wrong).

In order to get realistic ranges in a project containing multiple tasks, you have to do some tricky math. Fortunately, we do that math for you. All you have to do is supply “ballpark” estimates and LiquidPlanner will turn them into a schedule that reflects the realistic uncertainties you’ve defined.

We refer to these calculations as “Statistically Correct Rollups” because they are a rollup of the contained work that is… well… statistically correct.

## Mathematics Warning

The following contains mathematics that may frighten some folks (and may cause excitement of varying degrees among the pocket protector crowd).

LiquidPlanner takes the range you gave us and determines a standard deviation (σ) for the estimate as well as the expected value (also called the population mean). From the standard deviation we calculate the variance (v). These are then the basic values we use for all ensuing calculations.

The variance is a special beast because unlike the end points of the range, the variance of a series of estimates do sum. The expected values also sum. So to calculate the range for two tasks that follow each other we…

- Calculate the expected value (E) and variance (v) for each task
- Sum them up E
_{T}= E_{1}+ E_{2}and v_{T}= v_{1}+ v_{2} - Back-calculate the standard deviation (σ) of the total from the variance
- Report the range for the total as E
_{T}– σ to E_{T}+ σ

And bada-bing… you’ve got a statistically correct total.

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