776 CHAPTER 12 Statistics Profile in Mathematics Katherine K. Wallman From 1992 to 2017, Katherine Wallman served as the chief statistician of the U.S. Office of Management and Budget. In this capacity, she oversaw and coordinated U.S. federal statistical policies, standards, and programs; developed and advanced long-term improvements in federal statistical activities; and represented the U.S. government in international statistics organizations, including the United Nations and the Organization for Economic Cooperation and Development. In the United States, there are multiple agencies that actually produce statistics on which the country relies. For example, the Census Bureau provides population data; the Bureau of Economic Analysis provides national accounting data; and the National Center for Health Statistics provides data concerning health and well-being. In her capacity, Katherine Wallman set standards for a federal statistical establishment that comprises more than 70 agencies spread across every cabinet department. Number of Workers One-Way Commuting Distance Distance (miles) Histogram Frequency polygon 4 1118253239 5 10 15 20 25 Figure 12.9 Example 6 Commuting Distances The frequency distribution of the one-way commuting distances for 70 workers is listed in Table 12.2. Construct a histogram and then construct a frequency polygon. Table 12.2 Distance (miles) Number of Workers 1–7 15 8–14 24 15–21 13 22–28 8 29–35 5 36 – 42 5 Solution The histogram can be constructed with either class limits or class marks (class midpoints) on the horizontal scale. Frequency polygons are constructed with class marks on the horizontal scale. Since we will construct a frequency polygon on the histogram, we will use class marks. Recall that class marks are determined by adding the lower class limit and upper class limit and dividing the sum by 2. For the first class, the class mark is , 1 7 2 + or 4. Since the class widths are seven units, the class marks will also differ by seven units (see Fig. 12.9). Now try Exercise 35 7 Example 7 Carry-on Luggage Weights The histogram in Fig. 12.10 shows the weights of selected pieces of carry-on luggage at an airport. Construct the frequency distribution from the histogram in Fig. 12.10. 10 9 8 7 6 5 4 3 2 1 Number of Pieces of Luggage Weights of Selected Pieces of Carry-on Luggage Weight (pounds) 3 8 131823283338 Figure 12.10 Shim Harno/Alamy Stock Photo
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