Constructing meaning for distribution: Investigating how college students organize and interpret data during statistical analysis

The purpose of this study was to investigate how college students make sense of data during statistical analysis and to develop a framework for understanding their reasoning in the context of data-based arguments. The study focused on how college students organize and interpret sets of data and how they use inscriptions of the data to develop data-based arguments. Eight semi-unstructured interviews were conducted in which students participated in three tasks. The tasks involved comparing two univariate sets of data by interpreting inscriptions of the data in light of an overarching question about the data. For each task, the data generation process and the subject's expectations regarding data organization were discussed prior to the subject viewing four different inscriptions of the data. A subject's interpretation of an inscription with regard to how the data were distributed was of special interest to the study.;A framework of reasoning patterns was developed by analyzing four of the interviews. The subjects' reasoning in the remaining four interviews could be explained by using the constructs of the framework. The first pattern of reasoning in the framework contrasts reasoning about the data sets in terms of an elementary understanding of typicality that circumvents the variability of data values and thus how the data values are distributed. The second pattern of reasoning in the framework involves comparing the data sets by identifying modal clumps, clusters of data values that constitute the majority of the data set. In the analysis, a distinction was made between partitioning the modal clumps proportionally and partitioning them additively. The third pattern of reasoning in the framework contrasts ways of reasoning about how the data are distributed that involve identifying perceptual clusters of data values as opposed to a focus on the relative frequency of data values in the intervals. A focus on the relative frequency involves the ability to read how the data are distributed from a partitioned equal groups inscription, a precursor of the box plot, without the presence of individual data values on the inscription.