Some Class-Participation Demonstrations for Introductory Probability and Statistics

Most statistics courses at the college (or high school) level, whether conducted in departments of statistics, mathematics, psychology, or elsewhere, are taken as a requirement by students who, unfortunately, often have little interest in the subject. There are several excellent textbooks at this level, and lecture time is often used to present examples--including realistic applications of statistics and also simplified examples to clarify the key issues that are covered in the text and homeworks. We have found that the simplified examples can be effectively taught by involving students in participatory demonstrations, rather than the instructor merely lecturing at the blackboard. For a student who is not convinced of the relevance of mathematics, it is useful to see the statistical data or probability distribution actually constructed (rather than simply seeing the blackboard analysis of previously-gathered data). At this point, when counterintuitive results appear, the students are motivated to learn the methods of probability and statistics that can be used to explain real-world variation (see, e.g., Cobb, 1992; Hogg, 1992). Here, we present several demonstrations, all based on well-known statistical concepts, that we and our students have found thought-provoking. They are most effective for relatively small classes (fewer than 60 students); with a large lecture course, some of the demonstrations can be done in the discussion sections. The purpose of this article is to create a convenient resource for