External Representations for Data Distributions: In Search of Cognitive Fit

Stephanie Lem, Patrick Onghana, Lieven Verschaffel, and Wim Van Dooren

Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task between participants, and assessing how university students use such representations in comparing aspects of data distributions. Following a cognitive fit approach, we searched for matches between items and representations. Depending on the item, some representations led to better achievement than other representations. However, due to the low overall accuracy rates and various difficulties that students displayed in interpreting these representations, we cannot make strong claims regarding matches between items and representations.