66 CHAPTER 2 Exploring Data with Tables and Graphs The Pareto chart in Figure 2-8 and the pie chart in Figure 2-9a depict the same data in different ways, but the Pareto chart does a better job of showing the relative sizes of the different components. Graphics expert Edwin Tufte makes the following suggestion: Never use pie charts because they waste ink on components that are not data, and they lack an appropriate scale. Frequency Polygon A frequency polygon uses line segments connected to points located directly above class midpoint values. A frequency polygon is very similar to a histogram, but a frequency polygon uses line segments instead of bars. A variation of the basic frequency polygon is the relative frequency polygon, which uses relative frequencies (proportions or percentages) for the vertical scale. An advantage of relative frequency polygons is that two or more of them can be combined on a single graph for easy comparison, as in Figure 2-11. FIGURE 2-10 Frequency Polygon of Daily Commute Time in Los Angeles (minutes) See Figure 2-10 for the frequency polygon corresponding to the daily Los Angeles commute time summarized in the frequency distribution of Table 2-2 on page 45 (based on the data from the Chapter Problem). The heights of the points correspond to the class frequencies, and the line segments are extended to the right and left so that the graph begins and ends on the horizontal axis. CP YOUR TURN. Do Exercise 15 “Chicago Commute Times.” EXAMPLE 6 Frequency Polygon of Daily Commute Time in Los Angeles CP Figure 2-11 shows the relative frequency polygons for the daily commute times in Los Angeles, California, and Boise, Idaho, from Data Set 31 “Commute Times”. Figure 2-11 uses all of the 1000 commute times for Los Angeles and Boise and it is not based on the smaller sample of 50 Los Angeles commute times used in Table 2-2 and Example 6. Figure 2-11 shows that the Los Angeles commute times are somewhat longer (farther to the right in the graph) than those in Boise. This is expected, given the larger population density of Los Angeles. Relative Frequency Polygons: Daily Commute Times in Los Angeles and Boise EXAMPLE 7 T d si su Gender-Based Wage Discrimination Currently, women in the United States make 80 cents for every dollar that men make. Part of that discrepancy is due to the “motherhood penalty” and the “fatherhood bonus.” Studies have shown that mothers are perceived as being less capable and less devoted to their job, are paid less, and are less likely to be hired by potential employers. Conversely, men are more likely to be hired if they have children and they are paid more after they become fathers. Sociology professor Michelle Budig conducted a study showing that unmarried women without children earned 96 cents for every dollar earned by men, but married mothers earned only 76 cents for every dollar earned by men. The reality is that although male and female employees are not fundamentally different, women suffer financially from a cultural bias that has no foundation in real data. One factor that contributes to the gender gap in salaries: Employers’ final job offers are often influenced by information on the job applicant’s previous salary. A lower previous salary may result in a lower salary offer and vice versa. In this way, gender wage gaps can persist and grow over the course of a career. C w f
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