36 Chapter 2 Graphical Summaries of Data It is hard to tell from the lists of numbers whether the mileages have changed much between 2000 and 2009. What is needed are methods to summarize the data, so that their most important features stand out. One way to do this is by constructing graphs that allow us to visualize the important features of the data. In this chapter, we will learn how to construct many of the most commonly used graphical summaries. In the case study at the end of the chapter, you will be asked to use graphical methods to compare the mileages between 2000 cars and 2009 cars. SECTION 2.1 Graphical Summaries for Qualitative Data Objectives 1. Construct frequency distributions for qualitative data 2. Construct bar graphs 3. Construct pie charts Objective 1 Construct frequency distributions for qualitative data Frequency Distributions for Qualitative Data How do retailers analyze their sales data to determine which items are most popular? Table 2.1 presents a list compiled by a computer retailer. Four types of computers are sold: desktops, laptops, notebooks, and tablets. The list contains the types of computers sold to the last 50 customers. Table 2.1 Types of Computers Sold Tablet Laptop Laptop Laptop Laptop Laptop Laptop Notebook Desktop Laptop Notebook Desktop Laptop Laptop Laptop Laptop Notebook Notebook Desktop Laptop Desktop Laptop Tablet Notebook Tablet Notebook Notebook Tablet Laptop Desktop Laptop Laptop Laptop Laptop Desktop Desktop Notebook Laptop Desktop Laptop Desktop Tablet Desktop Laptop Laptop Desktop Tablet Notebook Tablet Laptop Table 2.1 is typical of data in raw form. It is a big list, and it’s hard to gather much information simply by looking at it. To make the important features of the data stand out, we construct summaries. The starting point for many summaries is a frequency distribution. DEFINITION • The frequency of a category is the number of times it occurs in the data set. • A frequency distribution is a table that presents the frequency for each category. EXAMPLE 2.1 Construct a frequency distribution Construct a frequency distribution for the data in Table 2.1. Solution To construct a frequency distribution, we begin by tallying the number of observations in each category and recording the totals in a table. Table 2.2 presents a frequency distribution for the computer sales data. We have included the tally marks in this table, but in practice it is permissible to omit them.
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