Section 2.3 More Graphs for Quantitative Data 63 Answers to Check Your Understanding Exercises for Section 2.2 1. Class Frequency 0.00–0.49 2 0.50–0.99 7 1.00–1.49 19 1.50–1.99 7 2.00–2.49 7 2.50–2.99 4 3.00–3.49 9 3.50–3.99 4 4.00–4.49 2 4.50–4.99 1 5.00–5.49 0 5.50–5.99 1 6.00–6.49 0 6.50–6.99 2 2. a. 15, 20, 25, 30, 35, 40 b. 5 c. 15 20 25 30 35 40 45 2500 2000 1500 1000 500 0 Frequency Age (years) d. Relative Age Frequency Frequency 15–19 795 0.110 20–24 2410 0.334 25–29 2190 0.304 30–34 1208 0.168 35–39 499 0.069 40–44 109 0.015 e. 15 20 25 30 35 40 45 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 Relative Frequency Age (years) 3. a. Skewed to the right b. Skewed to the left c. Approximately symmetric 4. a. Unimodal b. Unimodal c. Bimodal SECTION 2.3 More Graphs for Quantitative Data Objectives 1. Construct stem-and-leaf plots 2. Construct dotplots 3. Construct time-series plots Histograms and other graphs that are based on frequency distributions can be used to summarize both small and large data sets. For small data sets, it is sometimes useful to have a summary that is more detailed than a histogram. In this section, we describe some commonly used graphs that provide more detailed summaries of smaller data sets. These graphs illustrate the shape of the data set, while allowing every value in the data set to be seen. Objective 1 Construct stem-and-leaf plots Stem-and-Leaf Plots Stem-and-leaf plots are a simple way to display small data sets. For example, Table 2.13 on page 64 presents the U.S. Census Bureau projection for the percentage of the population aged 65 and over for each state and the District of Columbia in the year 2010. In a stem-and-leaf plot, the rightmost digit is the leaf, and the remaining digits form the stem. For example, the stem for Alabama is 14, and the leaf is 1.We construct a stem-and-leaf plot for the data in Table 2.13 by using the following three-step process: Step 1: Make a vertical list of all the stems in increasing order, and draw a vertical line to the right of this list. The smallest stem in Table 2.13 is 8, belonging to Alaska, and the largest is 17, belonging to Florida. The list of stems is shown in Figure 2.12(a) on page 64. Step 2: Go through the data set, and for each value, write its leaf next to its stem. For example, the first value is 14.1, for Alabama. We write a “1” next to the stem 14.
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