Chapter 3

• 3.1 The purpose of a graph is to reveal and clarify relations between variables.
• 3.2 Five miles per gallon change (from 22 to 27) and change
• 3.3 The graph on the left is misleading. It shows a sharp decline in annual traffic deaths in Connecticut from 1955 to 1956, but we cannot draw valid conclusions from just two data points. The graph on the right is a more accurate and complete depiction of the data. It includes nine, rather than two, data points and suggests that the sharp 1-year decline was the beginning of a clear downward trend in traffic fatalities that extended through 1959. It also shows that there had been previous 1-year declines of similar magnitude—from 1951 to 1952 and from 1953 to 1954. Also, the γ-axis does not go down to 0, which exaggerates any differences.
• 3.4 Scatterplots and line graphs both depict the relation between two scale variables.
• 3.5 We should typically avoid using pictorial graphs and pie charts because the data can almost always be presented more clearly in a table or in a bar graph.
• 3.6 The line graph known as a time plot or time series plot allows us to calculate or evaluate how a variable changes over time.
• 3.7
  • a. A scatterplot is the best graph choice to depict the relation between two scale variables such as depression and stress.
  • b. A time plot, or time series plot, is the best graph choice to depict the change in a scale variable, such as the rise or decline in the number of facilities over time.
  • c. For one scale variable, such as number of siblings, the best graph choice would be either a frequency histogram or frequency polygon.
  • d. In this case, there is a nominal variable (region of the United States) and a scale variable (years of education). The best choice would be a bar graph, with one bar depicting the mean years of education for each region. In a Pareto chart, the bars would be arranged from highest to lowest, allowing for easier comparisons.
  • e. Calories and hours are both scale variables, and the question is about prediction rather than relation. In this case, we would calculate and graph a line of best fit.
• 3.8 Chartjunk is any unnecessary information or feature in a graph that detracts from the viewer’s understanding.
• 3.9
  • a. Scatterplot or line graph
  • b. Bar graph
  • c. Scatterplot or line graph
• 3.10
  
  The accompanying graph improves on the chartjunk graph in several ways. First, it has a clear, specific title. Second, all axes are labeled left to right. Third, there are no abbreviations. The units of measurement, IQ and hours of sunlight per day, are included. The γ-axis has 0 as its minimum, the colors are simple and muted, and all chartjunk has been eliminated. This graph wasn’t as much fun to create, but it offers a far clearer presentation of the data! (Note: We are treating hours as an ordinal variable.)