[9] The Mean of a Sum

In addition to representing individual tasks, within our project models, we also need to represent sequences of tasks, and we need to estimate the likely duration of each sequence. This brings us to our second guideline: The mean of a sum equals the sum of the means. The expected duration of a sequence of tasks equals the sum of the expected durations of the individual tasks. This simple rule is illustrated in the next figure.


This guideline is always true, so long as we are talking about sequential tasks and not parallel tasks. But already it is becoming evident that we need to focus on much more than just the sum of task durations. Variation is a strong function of the number of tasks in a sequence, as the figure suggests. Therefore, let’s begin to explore the role that variation plays, as we strive to construct our predictive models of projects.