Students’ conceptions of average and standard deviation

As statistics teachers, we investigated undergraduate students’ conceptual understanding of two major measures of descriptive statistics, average and standard deviation. First, 352 students were asked to define average and standard deviation before their first statistics class. The answers confirmed that most of the students had an algorithmic conception of average and failed to explain what standard deviation is. We then focused on the way students’ understanding of average and standard deviation improved, which is still largely unexplored: so we repeated the same experiment after the last statistics lesson of the year. Students’ preconceptions seem to have disappeared after statistics teaching; the final results showed a better understanding of average and standard deviation with some lingering difficulties for standard deviation.