Week 2 Queue Lab: Find what the average hides

Work the Office of Everything's own ticket log against its "average wait" memo, then apply the same check to the system you are tracking yourself.

1 March 2027

The Office summarises this ten-ticket sample with one number: “Mean wait: 5 minutes. Service remains excellent.” Check the arithmetic, then ask what that correct number leaves out. A correct calculation does not establish that the service was excellent.

Before the lab#

Bring your own system’s data from week 1: even a rough sense of “this person waited about this long” is enough to start.

In the lab#

Office of Everything file — synthetic case material. Ticket log, Tuesday of week 2, front counter, times in minutes from taking a ticket to being served: 2, 3, 3, 2, 4, 3, 2, 26, 3, 2. These are ten waiting durations, not service durations. The memo summarises this sample only, not a month or the whole population.

Compute the mean and the median of that list by hand. They will not match. Work out why: one printer-credit dispute waited 26 minutes before service started. Its service duration and the cause of its wait are not recorded. The mean is 5 minutes and the median is 3; show your working before checking those values. Write a replacement memo reporting both and the longest wait. Neither summary alone proves that service is fair.

Then do the same arithmetic on your own real system’s numbers from this week’s observation. If your system doesn’t happen to have an outlier yet, say so — that is itself a finding, and you’ll get another chance to look next week.

Afterwards#

Keep both datasets. Week 3 first omits this sample’s longest wait, then uses a separate service-time log to investigate delays passed to later arrivals. Removing a number from a report does not remove a delay from the queue.