SECTION 2.1 Frequency Distributions and Their Graphs 43 Finding Midpoints, Relative Frequencies, and Cumulative Frequencies Using the frequency distribution constructed in Example 1, find the midpoint, relative frequency, and cumulative frequency of each class. Describe any patterns. SOLUTION The midpoints, relative frequencies, and cumulative frequencies of the first five classes are calculated as follows. Class f Midpoint Relative frequency Cumulative frequency 155–190 3 155 + 190 2 = 172.5 3 30 = 0.1 3 191–226 2 191 + 226 2 = 208.5 2 30 ≈ 0.07 3 + 2 = 5 227–262 5 227 + 262 2 = 244.5 5 30 ≈ 0.17 5 + 5 = 10 263–298 6 263 + 298 2 = 280.5 6 30 = 0.2 10 + 6 = 16 299–334 7 299 + 334 2 = 316.5 7 30 ≈ 0.23 16 + 7 = 23 The remaining midpoints, relative frequencies, and cumulative frequencies are shown in the expanded frequency distribution below. Frequency Distribution for Cell Phone Screen Times (in minutes) Class Frequency, f Midpoint Relative frequency Cumulative frequency 155–190 3 172.5 0.1 3 191–226 2 208.5 0.07 5 227–262 5 244.5 0.17 10 263–298 6 280.5 0.2 16 299–334 7 316.5 0.23 23 335–370 4 352.5 0.13 27 371–406 3 388.5 0.1 30 Σf = 30 Σ f n = 1 Times Number of adults Portion of adults Interpretation There are several patterns in the data set. For instance, the most common range for the times is 299 to 334 minutes. Also, about half of the times are less than 299 minutes. TRY IT YOURSELF 2 Using the frequency distribution constructed in Try It Yourself 1, find the midpoint, relative frequency, and cumulative frequency of each class. Describe any patterns. Answer: Page A35 EXAMPLE 2 For help with summation, see Integrated Review at MyLab Statistics
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