Section 3.1 Measures of Center 97 SECTION 3.1 Exercises Exercises 1–6 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 7–10, fill in each blank with the appropriate word or phrase. 7. The is calculated by summing all data values and dividing by how many there are. 8. The is a number that splits the data set in half. 9. The median is resistant because it is not affected much by . 10. The is the value in the data set that appears most frequently. In Exercises 11–14, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 11. Every data set contains at least one mode. 12. The mean is resistant. 13. For most data sets that are skewed to the right, the mean is less than the median. 14. A mode is always a value that is in the data set. Practicing the Skills 15. Find the mean, median, and mode for the following data set: 12 27 26 27 25 16. Find the mean, median, and mode for the following data set: −20 15 21 −20 19 17. Find the mean, median, and mode for the following data set: 28 −31 28 0 31 −23 18. Find the mean, median, and mode for the following data set: 83 98 22 89 99 98 In Exercises 19–22, use the given frequency distribution to approximate the mean. 19. Class Frequency 0–9 13 10–19 7 20–29 10 30–39 9 40–49 11 20. Class Frequency 0–15 2 16–31 14 32–47 6 48–63 13 64–79 15 21. Class Frequency 0–49 17 50–99 26 100–149 14 150–199 34 200–249 26 250–299 8 22. Class Frequency 0–19 18 20–39 11 40–59 6 60–79 6 80–99 10 100–119 5 23. Which is the correct mean and median for the following histogram? 3 4 5 6 7 8 9 0.5 0.4 0.3 0.2 0.1 0 Relative Frequency (i) Mean is 4.6; median is 5.0 (ii) Mean is 4.5; median is 4.2 (iii) Mean is 3.5; median is 4.3 (iv) Mean is 5.6; median is 5.3 24. Which is the correct mean and median for the following histogram? 0 1 2 3 4 5 6 7 8 0.25 0.20 0.15 0.10 0.05 0 Relative Frequency (i) Mean is 3.6; median is 4.8 (ii) Mean is 4.8; median is 3.6 (iii) Mean is 3.5; median is 3.1 (iv) Mean is 4.2; median is 4.1 25. Which is the correct mean and median for the following histogram? 2 3 4 5 6 7 8 9 10 11 12 13 14 0.20 0.15 0.10 0.05 0 Relative Frequency
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