On the misinterpretation of histograms and box plots

Abstract

Recent studies have shown that the interpretation of graphs is not always easy for students. In order to reason properly about distributions of data, however, one needs to be able to interpret graphical representations of these distributions correctly. In this study, we used Tversky’s principles for the design of graphs to explain how 125 first-year university students interpreted histograms and box plots. We systematically varied the representation that accompanied the tasks between students to identify how the design principles affected students’ reasoning. Many students displayed misinterpretations of histograms and box plots, despite the fact that they had the required knowledge and time to interpret the representations correctly. We argue that the combination of dual process theories and Tversky’s design principles provides a promising theoretical framework, which leads to various possibilities for future research.

Keywords:

• graphical representations
• statistics education
• problem solving
• reasoning
• data distribution

Acknowledgements

Stephanie Lem holds a PhD fellowship of the Research Foundation – Flanders (FWO). This research was partially supported by the grant G063709N “Representational adaptivity in mathematical thinking and learning: analysis and improvement” from the Fund for Scientific Research Flanders.

Notes

1. In this article, we will use ‘representation’ to refer to ‘external representation’.

2. We are aware of the fact that variations of the box plot exist in which the height of the box does indicate n. However, the students in our study were only taught about the standard box plot in which the height of the box does not reflect any information concerning the number of observations.