In short, even though instruction in statistics usually focuses on averages, many
students do not use those measures of central tendency when they would be
particularly helpful—to make comparisons between groups composed of variable
elements. We suggest that this pattern is symptomatic of students’ failure to interpret
an average of a data set as saying something about the entire distribution of values.
To address this problem instructionally, we believe that we should be encouraging
students early in statistics instruction to think of averages as central tendencies or
signals in noisy processes. We acknowledge that this is a complex idea and one that
is particularly difficult to apply to the type of processes that we often have students
investigating. We explore these conceptual difficulties below.