52 Chapter 2 Graphical Summaries of Data Check Your Understanding 1. Using the data in Table 2.7, construct a frequency distribution with classes of width 0.5. Answer is on page 63. Computing the class width for a given number of classes In Example 2.10, the first step in computing the frequency distribution was to choose a class width. Sometimes we begin by choosing an approximate number of classes instead. In these cases, we compute the class width as follows: Step 1: Decide approximately how many classes to have. Step 2: Compute the class width as follows: Class width = Largest data value − Smallest data value Number of classes Step 3: Round the class width to a convenient value. It is usually better to round up. Once the class width is determined, we proceed just as in the case where the class width is given.We choose a lower limit for the first class by choosing a convenient number that is slightly less than the minimum data value. We then compute the lower limits for the remaining classes, count the number of observations in each class, and construct the frequency distribution. Note that the actual number of classes may differ somewhat from the chosen number, because the class width is rounded and because the lower limit of the first class will generally be less than the smallest data value. EXAMPLE 2.11 Computing the class width Find the class width for a frequency distribution for the data in Table 2.7, if it is desired to have approximately seven classes. Solution Step 1: We will have approximately seven classes. Step 2: The smallest data value is 0.25 and the largest is 6.64.We compute the class width: Class width = 6.64 − 0.25 7 = 0.91 Step 3: We round 0.91 up to 1, since this is the nearest convenient number. We will use a class width of 1. A reasonable choice for the lower limit of the first class is 0. This choice will give us the frequency distribution in Table 2.8. Objective 2 Construct histograms Histograms Once we have a frequency distribution or a relative frequency distribution, we can put the information in graphical form by constructing a histogram. Histograms based on frequency distributions are called frequency histograms, and histograms based on relative frequency distributions are called relative frequency histograms. Histograms are related to bar graphs and are appropriate for quantitative data. A histogram is constructed by drawing a rectangle for each class. The heights of the rectangles are equal to the frequencies or the relative frequencies, and the widths are equal to the class width. The left edge of each rectangle corresponds to the lower class limit, and the right edge touches the left edge of the next rectangle. EXAMPLE 2.12 Construct a histogram Table 2.10 presents a frequency distribution and the relative frequency distribution for the particulate emissions data.
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