A Comparative Study of Student Understanding of Center and Variability in Graphical Displays

• Activity Number: 179 - Contributed Poster Presentations: Section on Statistical Education
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Amy Froelich* and Jennifer Kaplan and Alexander Lyford and Kathleen Rey
• Companies: Iowa State University and University of Georgia and UGA and Iowa State University
• Keywords: histograms ; descriptive statistics ; stem-and-leaf plots

Abstract

Prior research has shown students tend to have difficulty connecting measures of center and variability to the histogram of a quantitative variable. The source of this difficulty appears to be misconceptions about the histogram, including confusion about the definition of the horizontal and vertical axes. In this study conducted in a large multi-section introductory statistics course, we investigate students' ability to compare measures of center (mean and median) and variability (range, IQR, and standard deviation) for the data distribution of the same variable between two groups when presented with different types of displays (histograms, stem-and-leaf plots, lists of data) and different shapes of the data distributions. The results indicate that students perform significantly worse on comparisons of the IQR and standard deviation between the two data distributions and when the data distributions are displayed using histograms versus stem-and-leaf plots or lists of data. Student explanations of their responses support the connection between performance on these questions and misconceptions about graphical displays of a quantitative variable.