Understanding graphs and tables

Wainer, H.
Educational Researcher

This article states that there are two considerations for learning to graph data: 1) the structure of the phenomenon, and 2) the limitations of the format of graphical representation used. This paper provides historical examples of how graphic data has been used, highlights aspects of a display theory, and identifies concrete steps to improve the tabular quality of graphs. According to the author, a graph has the power to answer most commonly asked questions about data, and invite deeper questions as long as it is properly drawn. Bertin's (1973) levels of questions that can be asked from a graph are described. The first level deals with elementary questions which involve simple extractions of data from the graphs. The second level deals with intermediate questions. These refer to trends among multiple points in the data, and the identification of outliers. The third level involves overall questions which requires an understanding of the deep structure of the data in its totality, often comparing trends or groups in the data, and the overall message of what is being said in the picture. Questions that involve retrieving data from tables are almost always elementary questions. These only require that students understand discrete units of data. Wainer states that most tables do a disservice by confusing the kinds of data presented. Columns are often placed without much thought to the relevancy of their order. The order within the columns is similarly vulnerable to irrelevance. For example, criterion variables (like countries) are often presented in alphabetical order when they should be arranged on a concept that is more useful (like size of GNP or population). The author therefore recommends that rows and columns are ordered in a way that makes sense and that numbers be rounded off as much as possible.