Expectation versus Variation: Students' Decision Making in a Sampling Environment

A task adapted from one used by Tversky and Kahneman (1971) was used in an interview or questionnaire context with 122 students from Grade 3 to Grade 13. Two questions assessed student understanding of the relationship of a sample to a population and of the expected value of the arithmetic mean, with and without information on a single value from the sample. Combining responses to the two questions, increasingly complex hierarchical sequences were identified in the observed responses in relation to the expected value of the means, an expectation variable, and in relation to the degree that ideas about variation were used to support judgements, a variation variable. Using data from another task performed by 68 of the students, responses were associated with the observed development of understanding of sampling more generally, a basic sampling variable. Overall, the associations of levels of response among the variables was not strong, suggesting more explicit discussion of sampling issues is required in classrooms. © 2006 Taylor and Francis Group, LLC.