Goal: to understand that random distributions often produce clusters
Equipment needed: large floor map, counters, wire frame
Time required: 10 minutes
Randomness is difficult to intuit. People tend to assume that a group of points arranged randomly should spread out evenly. Consequently, any visible trend or cluster on a map of, say, cancer cases, is viewed with suspicion. Journalists may then search for data to support the pattern they see, and discover a new phone mast, or crematorium, or power line in the area.
To show students that clusters are a natural outcome of randomness, lay out a large map on the floor and have them gather around. Have one or two students sprinkle counters onto the map.
Tell the students that the dots represent incidences of disease. Using a small wire hoop or similar frame, isolate an area on the map that has a large number of counters.
"Ask the students why this area has such a high incidence of disease. Counter their suggestions by pointing out similar areas that do not have any disease incidence. Keep reminding the students that the disease incidence was cast “randomly”."
The lesson is that “random” is not the same as “evenly spread”. Close by instructing the students to be wary of automatically associating some cause or motive to incidents that might equally be explained by natural variation. In practice, this can be very difficult. Residents do not want to be told that the rash of cancers on their street has no explanation further than bad luck. It does not make a good story.
If you want to explore this topic further with them, lead into extremes and, for advanced students, the use of funnel charts and Poisson distribution.