Statistical Variation in a Chance Setting: A Two-Year Study

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing the understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to display appreciation of variation from point expectation and four questions address variation from distributional expectation. Three hundred and seventy-five students in Grades 3–9 answered some or all of these questions. These students then took part in a unit of study on chance and data emphasizing variation. Of these students, 334 answered a post-test including the same items and a further subset of 199 students completed a longitudinal survey of the same items two years later. Analysis of the initial data showed a progression of understanding across the years of schooling, plateauing at Grade 7, improvement for all grades after instruction, and generally sustained and continuing improved performance after two years. Educational issues are considered.