2.1 EXERCISES SECTION 2.1 Frequency Distributions and Their Graphs 49 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions? 2. Why should the number of classes in a frequency distribution be between 5 and 20? 3. What is the difference between class limits and class boundaries? 4. What is the difference between relative frequency and cumulative frequency? 5. After constructing an expanded frequency distribution, what should the sum of the relative frequencies be? Explain. 6. What is the difference between a frequency polygon and an ogive? True or False? In Exercises 7–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 7. In a frequency distribution, the class width is the distance between the lower and upper limits of a class. 8. The difference between two consecutive midpoints is equal to the class width. 9. A graph of the cumulative frequencies can decrease from left to right. 10. Class boundaries ensure that consecutive bars of a histogram touch. In Exercises 11–14, use the given information about the data set and the number of classes to find the class width, the lower class limits, and the upper class limits. 11. min = 9, max = 64, 7 classes 12. min = 12, max = 88, 6 classes 13. min = 17, range = 118, 8 classes 14. max = 247, range = 93, 10 classes Reading a Frequency Distribution In Exercises 15 and 16, use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries. 15. Travel Time to Work (in minutes) Class Frequency, f 0–10 188 11–21 372 22–32 264 33–43 205 44–54 83 55–65 76 66–76 32 16. Toledo, OH, Average Normal Temperatures 1 °F2 Class Frequency, f 25–32 86 33–40 39 41–48 41 49–56 48 57–64 43 65–72 68 73–80 40 17. Use the frequency distribution in Exercise 15 to construct an expanded frequency distribution, as shown in Example 2. 18. Use the frequency distribution in Exercise 16 to construct an expanded frequency distribution, as shown in Example 2.
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