Page 1 of 5 Mean, Median, and Mode BEFORE Now WHY? You compared and ordered whole numbers and decimals. You’ll describe data using mean, median, and mode. So you can find average auto racing speeds, as in Ex. 21. In the Real World Word Watch mean, p. 101 median, p. 101 mode, p. 101 range, p. 102 Geysers Over a span of 12 hours, Old Faithful Geyser in Yellowstone National Park erupted 10 times. The lengths, in minutes, of the eruptions are shown below. 2.8 4.5 4.1 3.7 3.5 4.5 2.2 4.9 2.6 4.2 What is the average length of the eruptions? Averages The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values. The mode of a data set is the value that occurs most often. A data set can have no mode, one mode, or more than one mode. EXAMPLE 1 Finding a Mean To find the mean length of the eruptions of Old Faithful listed above, divide the sum of the 10 lengths by 10. 2.8 4.5 4.1 3.7 3.5 4.5 2.2 4.9 2.6 4.2 Mean 10 37 10 3.7 ANSWER The mean length of the eruptions is 3.7 minutes. Lesson 3.1 Mean, Median, and Mode 101 Page 2 of 5 Range To describe how spread out data are, you can find the range. The range of a data set is the difference between the greatest value and the least value. EXAMPLE 2 Finding Median, Mode, and Range Find the median, mode(s), and range of the numbers below. with 64 60 64 38 52 65 61 48 Review Need help with ordering whole numbers? See p. 682. Write the numbers in order from least to greatest. 38 48 52 60 61 64 64 65 Median: Because there is an even number of data values, the median is the mean of the two middle values. 60 61 2 121 2 Median 60.5 Mode: The number that occurs most often is 64. Range: Find the difference between the greatest and the least values. Range 65 38 27 Your turn now Find the mean, median, mode(s), and range. 1. 9, 13, 19, 14, 16, 11, 7, 6, 13 EXAMPLE 3 2. 18, 52, 23, 79, 66, 17, 20, 10 Choosing the Best Average Dance-a-Thon You receive the pledge amounts listed below for your participation in a dance-a-thon. Which average best represents the pledge amounts? $1 $8 $12 $10 $45 $9 $1 $7 $6 Solution Compare the mean, median, and mode. Mean: 1 8 12 10 45 9 1 7 6 $11 9 Median: 1 1 6 7 8 9 10 12 45 The median is $8. Mode: The pledge that occurs most often is $1. The mean suggests that the pledges are greater than they actually are. The mode suggests that the pledges are less than they actually are. ANSWER The median best represents the pledge amounts. 102 Chapter 3 Data and Statistics Page 3 of 5 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 707 Getting Ready to Practice Vocabulary Tell whether the statement is true or false. 1. The value that occurs the most often in a data set is the mode. 2. The range of a data set is the sum of the greatest and the least values. Televisions The data below are the number of televisions that 11 students have in their homes. 3 2 1 1 1 5 3 1 2 1 2 3. Find the mean. 4. Find the median. 5. Find the mode(s). 6. Find the range. 7. Find the Error Describe median and correct the error in finding the median of the data set. 10, 11, 24, 45, 41, 15, 45, 24, 50 Practice and Problem Solving with Example 1 2 3 Homework Exercises 8–18 8–18 19, 21, 25–26 Online Resources CLASSZONE.COM • More Examples • eTutorial Plus Find the mean, median, mode(s), and range of the data. 8. 17, 30, 38, 38, 42 9. 4, 4, 8, 11, 12, 16, 22 10. 108, 490, 502, 502, 502, 518 11. 20, 26, 31, 42, 44, 47, 51, 75 12. 46, 23, 63, 23, 81, 75, 46 13. 9, 63, 87, 45, 8, 87, 25, 12 14. 1.1, 0, 3, 2.8, 4.6 15. 7.6, 7.6, 6.1, 6, 14.3 16. 5.1, 5.3, 5.1, 5.2, 5.2, 5.3, 5.2 17. 68.4, 65.7, 63.9, 79.5, 52.5 Earrings In Exercises 18 and 19, use the following information. Sixteen 12-year-old girls were asked how many pairs of earrings they own. The results are listed below. 23, 27, 12, 20, 11, 9, 5, 10, 16, 32, 14, 31, 13, 8, 37, 32 18. Find the mean, median, and mode(s) of the data. 19. Which average best represents the data? Explain your reasoning. 20. Critical Thinking Is it possible for the mean, median, and mode of a data set to be the same number? If so, give an example. Lesson 3.1 Mean, Median, and Mode 103 Page 4 of 5 21. Indy 500 The table shows Sports the speeds of the fastest qualifiers in the Indy 500 each year for 1996–2001. Find the median and mean rounded to the nearest thousandth. Which average better represents the speeds? 22. Find the mode(s) of the following words: red, yellow, red, blue, blue, yellow, red, blue, yellow, red. Why is only the mode appropriate? Speed (miles per hour) Year Name 1996 Scott Brayton 236.986 1997 Arie Luyendyk 218.263 1998 Billy Boat 223.503 1999 Arie Luyendyk 225.179 2000 Greg Ray 223.471 2001 Scott Sharp 226.037 23. School Newspaper Use the excerpt from a school newspaper to identify the mean, mode(s), and range of hours spent on homework. ■ Indy 500 In 1911, it took Ray Harroun about 6 hours 42 minutes to win the first Indy 500. In 2000, it took Juan Montoya, pictured above, about 2 hours 59 minutes to win. About how much longer did it take Harroun than Montoya to win? The student council surveyed students about the number of hours they spend on homework each night. The responses spanned 3 hours, falling between 0 hours and 3 hours. The typical response was 1.5 hours, and the most frequent response was 1 hour. Comic Book Club The line plot at the right shows the ages of students in a comic book club. 24. Find the mean, median, and mode(s) of the data. 10 11 12 13 14 15 25. Which average best represents the data? Explain your reasoning. with Review Test Scores Sally’s scores on her science quizzes are listed below. Need help with reading line plots? See p. 704. 86 78 70 68 95 81 85 89 95 26. Which average best represents Sally’s scores? Explain your reasoning. 27. Sally receives a score of 100 on the next quiz. How does this score affect the mean, median, and mode(s) of Sally’s scores? Algebra Find the value of x that makes the mean the given number. 28. 5, 8, 9, 4, 1, x; mean 5 29. 12, 7, 18, 15, 11, 9, x; mean 12 30. Challenge Find five numbers with a mean of 16, a median of 15, a mode of 21, and a range of 11. 104 Chapter 3 Data and Statistics Page 5 of 5 Mixed Review Copy and complete the statement. (Lesson 2.7) 31. 5 kg _?_ g 32. 3.7 m _?_ cm 33. 480 mL _?_ L Choose a Strategy Use a strategy from the list to solve the following problem. Explain your choice of strategy. Problem Solving Strategies Look for a Pattern Estimate ■ Work Backward ■ ■ 34. You are buying art supplies to make signs for a car wash. Each piece of poster board costs $1.20, and a package of markers costs $3.88. Will $15 cover the cost of 10 pieces of poster board and 2 packages of markers? Basic Skills Find the product or quotient. 35. 65 19 36. 729 9 37. 583 11 Test-Taking Practice INTERNET State Test Practice 38. Multiple Choice The amount of money you earned each week from baby-sitting is listed below. Find the mean of the data. CLASSZONE.COM $15 $20 $10 $15 $20 $15 $15 $10 A. $10 B. $15 C. $20 D. $25 39. Short Response The ages of the players on your baseball team are as follows: 10, 11, 11, 12, 12, 12, 13, 13, 13, 13. Your friend says the 13 10 2 mean age of the players is 11.5 years because 11.5. Do you agree with your friend? Explain your reasoning. What’s my age? Use the following clues to find the age of each member of a family of five. The median is 12. The mean is 21. The mode is 41. The age of one of the family members is the median divided by 3. Lesson 3.1 Mean, Median, and Mode 105