50 Chapter 2 Graphical Summaries of Data We can now compute the relative frequency for each class. For the class 0.00–0.99, the frequency is 9. The relative frequency is therefore Relative frequency = Frequency Sum of all frequencies = 9 65 = 0.138 Table 2.9 is a relative frequency distribution for the data in Table 2.7. The frequencies are shown as well. Table 2.9 Relative Frequency Distribution 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 Choosing the classes In Examples 2.7 and 2.8, we chose the classes to be 0.00–0.99, 1.00–1.99, and so on. There are many other choices we could have made. For example, we could have chosen the classes to be 0.00–1.99, 2.00–3.99, 4.00–5.99, and 6.00–7.99. As another example, we could have chosen them to be 0.00–0.49, 0.50–0.99, and so on, up to 6.50–6.99. We now define some of the terminology that we will use when discussing classes. DEFINITION • The lower class limit of a class is the smallest value that can appear in that class. • The upper class limit of a class is the largest value that can appear in that class. • The class width is the difference between consecutive lower class limits. CAUTION The class width is the difference between the lower limit and the lower limit of the next class, not the difference between the lower limit and the upper limit. Class limits should be expressed with the same number of decimal places as the data. The data in Table 2.7 are rounded to two decimal places, so the class limits for these data are expressed with two decimal places as well. EXAMPLE 2.9 Find the class limits and widths Find the lower class limits, the upper class limits, and the class widths for the relative frequency distribution in Table 2.9. Solution The classes are 0.00–0.99, 1.00–1.99, and so on, up to 6.00–6.99. The lower class limits are therefore 0.00, 1.00, 2.00, 3.00, 4.00, 5.00, and 6.00. The upper class limits are 0.99, 1.99, 2.99, 3.99, 4.99, 5.99, and 6.99. We find the class width for the first class by subtracting consecutive lower limits: Class width = Lower limit for second class − Lower limit for first class = 1.00 − 0.00 = 1.00 Similarly, we find that all the classes have a width of 1. When constructing a frequency distribution, there is no one right way to choose the classes. However, there are some requirements that must be satisfied:
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