12.4 Measures of Dispersion 805 e) What is the approximate standard deviation of boys’ weights at age 17? ≈ 40 lb f) Assuming that this chart was constructed so that approximately 95% of all boys are always in the normal range, determine what percentage of boys are not in the normal range. 5% 35. Athletes’ Salaries The following tables list the 10 highestpaid athletes in Major League Baseball and in the National Football League. Major League Baseball (2023 Season) Player Annual Salary (millions of dollars) 1. Max Scherzer 43.3 2. Justin Verlander 43.3 3. Aaron Judge 40.0 4. Anthony Rendon 38.6 5. Mike Trout 37.1 6. Gerrit Cole 36.0 7. Cory Seager 35.5 8. Nolan Arenado 35.0 9. Stephen Strasburg 35.0 10. Francisco Lindor 34.1 Source: MLB.com National Football League (2023 – 2024 Season) Player Annual Salary (millions of dollars) 1. Lamar Jackson 52.0 2. Jalen Hurts 51.0 3. Aaron Rodgers 50.3 4. Russell Wilson 49.0 5. Kyler Murray 46.1 6. Deshaun Watson 46.0 7. Patrick Mahomes 45.0 8. Josh Allen 43.0 9. Dak Prescott 40.0 10. Daniel Jones 40.0 Source: NFL.com a) Without doing any calculations, which do you believe is greater, the mean salary of the 10 baseball players or the mean salary of the 10 football players? Answers will vary. b) Without doing any calculations, which do you believe is greater, the standard deviation of the salary of the 10 baseball players or the standard deviation of the salary of the 10 football players? Answers will vary. c) Compute the mean salary of the 10 baseball players and the mean salary of the 10 football players and determine whether your answer in part (a) was correct. Round each mean to the nearest tenth of a million dollars. MLB: $37.8 million, NFL: $46.2 million d) Compute the standard deviation of the salary of the 10 baseball players and the standard deviation of the salary of the 10 football players and determine whether your answer in part (b) is correct. Round each standard deviation to the nearest tenth. MLB: ≈ $3.4 million; NFL: ≈ $4.3 million 36. Oil Change Jiffy Lube has franchises in two different parts of a city. The number of oil changes made daily, for 25 days, is given below. East Store West Store 33 59 27 30 42 38 46 38 38 30 19 42 25 22 32 38 38 37 39 31 43 27 57 37 52 39 36 40 37 47 40 67 38 44 43 30 34 42 45 29 15 31 49 41 35 31 46 28 45 48 a) Construct a frequency distribution for each store with a first class of − 15 20. * b) Draw a histogram indicating the number of oil changes at each store. * c) Using the histograms, determine which store appears to have a greater mean, or do the means appear about the same? Explain. They appear to have about the same mean, since they are both centered around 38. d) Using the histogram, determine which store appears to have the greater standard deviation. Explain. The distribution for East is more spread out. Therefore, East has a greater standard deviation. e) Calculate the mean for each store and determine whether your answer in part (c) was correct. East: 38, West: 38 f) Calculate the standard deviation for each store and determine whether your answer in part (d) was correct. East: ≈ 12.64, West: ≈ 5.98 Recreational Mathematics 37. Measures of Dispersion Calculate the range and standard deviation of your exam grades in this mathematics course. Round the mean to the nearest tenth to calculate the standard deviation. Answers will vary. 38. Measures of Central Tendency Construct a set of five pieces of data with a mean, median, mode, and midrange of 6 and a standard deviation of 0. 6, 6, 6, 6, 6 Research Activity 39. Salaries Using the Internet, determine the current 10 highest-paid CEOs in each of the following: Tech companies, Healthcare companies, and Retailers. Determine the mean and the standard deviation of each group. 40. Variance Another measure of dispersion is variance. Do research and write a report on variance. Explain how to calculate variance, and explain the relationship between variance and standard deviation. $ $ *See Instructor Answer Appendix
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