STATISTICS IN SUMMARY
Chapter Specifics
• To see what data say, start with graphs.
• The choice of graph depends on the type of data. Do you have a categorical variable, such as level of education or occupation, which puts individuals into categories? Or do you have a quantitative variable measured in meaningful numerical units?
• Check data presented in a table for roundoff errors.
• The distribution of a variable tells us what values it takes and how often it takes those values.
• To display the distribution of a categorical variable, use a pie chart or a bar graph. Pie charts always show the parts of some whole, but bar graphs can compare any set of numbers measured in the same units. Bar graphs are better for comparisons. Bar graphs can be displayed vertically or horizontally.
• To show how a quantitative variable changes over time, use a line graph that plots values of the variable (vertical scale) against time (horizontal scale). If you have values of the variable for different categories, use a separate line for each category. Look for trends and seasonal variation in a line graph, and ask whether the data have been seasonally adjusted.
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• Graphs can mislead the eye. Avoid pictograms that replace the bars of a bar graph by pictures whose height and width both change. Look at the scales of a line graph to see if they have been stretched or squeezed to create a particular impression. Avoid clutter that makes the data hard to see.
In reasoning from data to a conclusion, where the data come from is important. We studied this in Chapters 1 through 9. Once we have the data, and are satisfied that they were produced appropriately, we can begin to determine what the data tell us. Tables and graphs help us do this. In this chapter, we learned some basic methods for displaying data with tables and graphs. We learned what information these graphics provide. An important type of information is the distribution of the data—the values that occur and how often they occur. The concept of the distribution of data or the distribution of a variable is a fundamental way that statisticians think about data. We will encounter it again and again in future chapters.
Data that are produced badly can mislead us. Likewise, graphs that are produced badly can mislead us. In this chapter, we learned how to recognize bad graphics. Developing “graphic sense,’’ the habit of asking if a graphic accurately and clearly displays our data, is as important as developing “number sense,’’ discussed in Chapter 9.
CASE STUDY EVALUATED Look again at Figure 10.1, described in the Case Study that opened the chapter. Based on what you have learned, is Figure 10.1 the best graphical representation of the top five leading causes of death across four major age categories? What are the drawbacks to the current graphical display? Discuss which graphical display would be better and why. If you have access to statistical software, create the graphical display you think is better.
Online Resources
• The Snapshots video Visualizing and Summarizing Categorical Data discusses categorical data and describes pie charts and bar graphs to summarize categorical data in the context of data from a NASA program.
• The StatClips video Summaries and Pictures for Categorical Data discusses how to draw a pie chart and a bar graph using two examples.
• The StatClips Example video Summaries and Pictures for Categorical Data Example A discusses pie charts and bar graphs in the context of data about the choice of field of study by first-year students.
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• The StatClips Example video Summaries and Pictures for Categorical Data Example B discusses bar graphs in the context of data from a survey about high-tech devices.
• The StatClips Example video Summaries and Pictures for Categorical Data Example C discusses the use of pie charts and bar graphs in the context of data from the Arbitron ratings.