This article describes a classroom activity designed to stimulate students to think creatively about methods of selecting a representative sample from a population. Students are presented with a data set consisting of gender, SAT verbal score, SAT mathematics score, and high school grade point average for 317 freshmen from North Carolina State University. The students, who have not yet studied sampling, work in groups of three or four to generate three possible methods for selecting a representative sample of 20 freshmen from the population of 317. Each group uses its proposed methods to select three samples and computes various summary statistics and plots for the variables in each sample. The students are then given corresponding information for the entire population. After comparing sample statistics and population parameters, the groups evaluate the advantages and disadvantages of the proposed sampling methods. During the two semesters that I have used this activity in my Statistics 101 class, students have "invented" simple random sampling, systematic sampling, stratified sampling, and various combinations thereof.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education