Section 2.2 Frequency Distributions and Their Graphs 49 To summarize these data, we will construct a frequency distribution. Since these data are quantitative, there are no natural categories. We therefore divide the data into classes. The classes are intervals of equal width that cover all the values that are observed. For example, for the data in Table 2.7, we could choose the classes to be 0.00–0.99, 1.00–1.99, and so forth. We then count the number of observations that fall into each class, to obtain the class frequencies. EXAMPLE 2.7 Construct a frequency distribution Explain It Again Frequency distributions for quantitative and qualitative data: Frequency distributions for quantitative data are just like those for qualitative data, except that the data are divided into classes rather than categories. Construct a frequency distribution for the data in Table 2.7, using the classes 0.00–0.99, 1.00–1.99, and so on. Solution First we list the classes. We begin by noting that the smallest value in the data set is 0.25 and the largest is 6.64. We list classes until we get to the class that contains the largest value. The classes are 0.00–0.99, 1.00–1.99, 2.00–2.99, 3.00–3.99, 4.00–4.99, 5.00–5.99, and 6.00–6.99. Since the largest number in the data set is 6.64, these are enough classes. Now we count the number of observations that fall into each class. The first class is 0.00–0.99. We count nine observations between 0.00 and 0.99 in Table 2.7. The next class is 1.00–1.99. We count 26 observations in this class. We repeat this procedure with classes 2.00–2.99, 3.00–3.99, 4.00–4.99, 5.00–5.99, and 6.00–6.99. The results are presented in Table 2.8. This is a frequency distribution for the data in Table 2.7. Table 2.8 Frequency Distribution for Particulate Data Class Frequency 0.00–0.99 9 1.00–1.99 26 2.00–2.99 11 3.00–3.99 13 4.00–4.99 3 5.00–5.99 1 6.00–6.99 2 We can also construct a relative frequency distribution. As with qualitative data, the relative frequency of a class is the frequency of that class, divided by the sum of all the frequencies. DEFINITION The relative frequency of a class is given by Relative frequency = Frequency Sum of all frequencies EXAMPLE 2.8 Construct a relative frequency distribution Construct a relative frequency distribution for the data in Table 2.7, using the classes 0.00–0.99, 1.00–1.99, and so on. Solution The frequency distribution is presented in Table 2.8. We compute the sum of all the frequencies: Sum of all frequencies = 9 + 26 + 11 + 13 + 3 + 1 + 2 = 65
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