The Effects of Data and Graph Type on Concepts and Visualizations of Variability

Abstract

Recognizing and interpreting variability in data lies at the heart of statistical reasoning. Since graphical displays should facilitate communication about data, statistical literacy should include an understanding of how variability in data can be gleaned from a graph. This paper identifies several types of graphs that students typically encounter—histograms, distribution bar graphs, and value bar charts. These graphs all share the superficial similarity of employing bars, and yet the methods to perceive variability in the data differ dramatically. We provide comparisons within each graph type for the purpose of developing insight into what variability means and how it is evident within the data's associated graph. We introduce graphical aids to visualize variability for histograms and value bar charts, which could easily be tied to numerical estimates of variability.

• Descriptive statistics
• Histograms
• Bar graphs
• Value bar charts
• Time plots
• Misconceptions