Section 2.2 Frequency Distributions and Their Graphs 55 Check Your Understanding 2. Following is a frequency distribution that presents the number of live births to women aged 15–44 in the state of Wyoming in a recent year. Distribution of Births by Age of Mother Age Frequency 15–19 795 20–24 2410 25–29 2190 30–34 1208 35–39 499 40–44 109 Source: Wyoming Department of Health a. List the lower class limits. b. What is the class width? c. Construct a frequency histogram. d. Construct a relative frequency distribution. e. Construct a relative frequency histogram. Answers are on page 63. Open-ended classes It is sometimes necessary for the first class to have no lower limit or for the last class to have no upper limit. Such a class is called open-ended. Table 2.11 presents a frequency distribution for the number of deaths in the United States due to pneumonia in a recent year for various age groups. Note that the last age group is “85 and older,” an open-ended class. Table 2.11 Deaths Due to Pneumonia Age Number of Deaths 5–14 69 15–24 178 25–34 299 35–44 875 45–54 1872 55–64 3099 65–74 6283 75–84 17,775 85 and older 27,758 Source: U.S. Census Bureau When a frequency distribution contains an open-ended class, a histogram cannot be drawn. Histograms for discrete data When data are discrete, we can construct a frequency distribution in which each possible value of the variable forms a class. Then we can draw a histogram in which each rectangle represents one possible value of the variable. Table 2.12 on page 56 presents the results of a hypothetical survey in which 1000 adult women were asked how many children they had. Number of children is a discrete variable, and in this data set, the values of this variable are 0 through 8. To construct a histogram, we draw rectangles of equal width, centered at the values of the variables. The rectangles should be just wide enough to touch. Figure 2.9 on page 56 presents a histogram.
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