Section 2.2 Frequency Distributions and Their Graphs 53 Construct a frequency histogram based on the frequency distribution in Table 2.10. Construct a relative frequency histogram based on the relative frequency distribution in Table 2.10. Table 2.10 Frequency and Relative Frequency Distributions for Particulate Data Class Frequency Relative Frequency 0.00–0.99 9 0.138 1.00–1.99 26 0.400 2.00–2.99 11 0.169 3.00–3.99 13 0.200 4.00–4.99 3 0.046 5.00–5.99 1 0.015 6.00–6.99 2 0.031 Solution We construct a rectangle for each class. The first rectangle has its left edge at the lower limit of the first class, which is 0.00, and its right edge at the lower limit of the next class, which is 1.00. The second rectangle has its left edge at 1.00 and its right edge at the lower limit of the next class, which is 2.00, and so on. For the frequency histogram, the heights of the rectangles are equal to the frequencies. For the relative frequency histogram, the heights of the rectangles are equal to the relative frequencies. Figure 2.5 presents a frequency histogram, and Figure 2.6 presents a relative frequency histogram, for the data in Table 2.10. Note that the two histograms have the same shape. The only difference is the scale on the vertical axis. 0 1 2 3 4 5 6 7 30 25 20 15 10 5 0 Frequency Particulate Emissions Figure 2.5 Frequency histogram for the frequency distribution in Table 2.10 0 1 2 3 4 5 6 7 0.5 0.4 0.3 0.2 0.1 0 Relative Frequency Particulate Emissions Figure 2.6 Relative frequency histogram for the relative frequency distribution in Table 2.10 Explain It Again Choosing the number of classes: There is no single right way to choose classes for a histogram. Use your best judgment to construct a histogram with an appropriate amount of detail. How should I choose the number of classes for a histogram? There are no hard-and-fast rules for choosing the number of classes. In general, it is good to have more classes rather than fewer, but it is also good to have reasonably large frequencies in some of the classes. The following two principles can guide the choice: • Too many classes produce a histogram with too much detail, so that the main features of the data are obscured. • Too few classes produce a histogram lacking in detail. Figures 2.7 and 2.8 on page 54 illustrate these principles. Figure 2.7 presents a histogram for the particulate data where the class width is 0.1. This narrow class width results in a large number of classes. The histogram has a jagged appearance, which distracts from the overall shape of the data. On the other extreme, Figure 2.8 presents a histogram for these
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