Chapter 2: Exploring Data with Tables and Graphs

Students learn to determine appropriate class limits, boundaries, and midpoints, as well as how to select an optimal number of classes and calculate class width to ensure meaningful summaries. The chapter emphasizes constructing frequency tables that show both absolute frequencies and relative frequencies, alongside cumulative frequencies that track the accumulation of observations across successive classes. Visual representation becomes central through multiple graphical methods suited to different data types: histograms and frequency polygons for continuous numerical data, ogives for cumulative distributions, and specialized tools like dotplots and stem-and-leaf displays that preserve individual data values while revealing distribution shape. For categorical data, bar graphs, Pareto charts, and pie charts provide effective communication of proportions and rankings. The chapter explores important distribution shapes including uniform, normal, and skewed distributions, noting how these patterns inform statistical interpretation. A critical section addresses how outliers and extreme values can distort visual presentations and mislead interpretation. The chapter also covers scatterplots as tools for displaying relationships between paired variables. Throughout, significant emphasis is placed on recognizing and avoiding misleading graphs through improper scaling, truncated axes, selective data presentation, and distorted visual proportions. Students develop skills in critical evaluation of statistical graphics encountered in media and research, learning to identify deceptive practices. The final focus prepares students to apply best practices when creating their own visualizations, ensuring clarity, accuracy, and honest representation of data.