In this article, we argue that the focus on centers and distributions in current statistics instruction isn't too excessive, but rather of the wrong kind. Exploration of centers ought to be seen as part of a study of characteristics of complex, variable processes; too frequently, centers are portrayed as little more than summaries of groups of values. To highlight this difference, we examine how statisticians use and think about measures of center to compare two groups, and contrast this with what researchers have observed students doing. We also present various commonly-held interpretations of averages and show how most of these interpretations provide little or no conceptual basis for comparing groups. Based on our analyses, we offer several recommendations about how to help students come to see measures of center and spread as co-constructed ideas.
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