Week 2: What does an average hide?

Why a single average wait time can be true and still misleading, and what it hides about who actually waits the longest.

1 March 2027

A number like “average wait: 5 minutes” is not false. It is also not the whole system. This lecture is about the gap between a summary statistic and the distribution it summarises, and why that gap is where a queue’s real costs usually hide.

Outline#

• mean versus median: what each one is actually telling you, and why they diverge exactly when a queue is least well-behaved
• the long tail, demonstrated: in this week’s ten-ticket log, nine tickets cluster near the average and one sits far outside it — enough to show how a single long wait can coexist with a fair-sounding average, without claiming every queue’s tail looks like this one
• who the average hides, in this case: the log’s one long wait belongs to a specific kind of request, not an arbitrary one — enough to raise the question of whether that pattern generalises, which this course does not assume without more evidence
• reading a distribution honestly, without needing more than counting and sorting

Office of Everything file — synthetic case material. A memo from the Office’s front counter, Tuesday of week 2: “Mean wait for this ten-ticket sample: 5 minutes. Service remains excellent.” The Queue Lab checks the calculation and what this sample can establish. It is not a monthly or population estimate; service durations and causes are unrecorded.

This week’s Queue Lab gives you that ticket log and asks you to find the story the memo left out — then asks you to do the same thing to the real system you started watching in week 1.