This paper develops insights into how to deal with the arithmetic mean in the initial phases of statistics instruction. It focuses on one of the various ways in which the mean can be used in statistics: as a normalized ratio. The paper analyzes individual interviews of 12 12-year-old students prior to their participation in a classroom teaching experiment. These interviews were used to test and develop instructional conjectures about how to support students' understanding of the mean and other normalized ratios. Three differences where detected in how students seemed to make sense of proportional comparison problems in which the use of the mean as a ratio is pertinent. The paper explains how these findings can be capitalized upon in designing and conducting instruction.
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