Finding and Discussing the Mean, Median, and

Midrange Another measure of central tendency that is rarely used but is easy to calculate is the midrange. It can be found by using the formula \(\text { Midrange }=\frac{(\text { Maximum data entry })+(\text { Minimum data entry })}{2}\) Which of the manufacturers in Exercise 63 would prefer to use the midrange statistic in their ads? Explain your reasoning. Equation Transcription: Text Transcription: Midrange =\frac(\text Maximum data entry )+( Minimum data entry )2

Problem 1A Specify the lower limit to be 1 and the upper limit to be 50. Add at least 10 points that range from 20 to 40 so that the mean and the median are the same. What is the shape of the distribution? What happens at first to the mean and the median when you add a few points that are less than 10? What happens over time as you continue to add points that are less than 10?

Problem 2A Specify the lower limit to be 0 and the upper limit to be 0.75. Place 10 points on the plot. Then change the upper limit to 25. Add 10 more points that are greater than 20 to the plot. Can the mean be any one of the points that were plotted? Can the median be any one of the points that were plotted? Explain

Problem 1E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.

Problem 2E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. Some quantitative data sets do not have medians.

Problem 3E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. A data set can have the same mean, median, and mode.

Problem 4E True or False In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. When each data class has the same frequency, the distribution is symmetric.

Problem 6E Constructing Data Sets In Exercise, construct the described data set. The entries in the data set cannot all be the same. Mean and mode are the same.

Problem 5E Constructing Data Sets In Exercise, construct the described data set. The entries in the data set cannot all be the same. Median and mode are the same.

Problem 7E Constructing Data Sets In Exercise, construct the described data set. The entries in the data set cannot all be the same. Mean is not representative of a typical number in the data set.

Problem 8E Constructing Data Sets In Exercise, construct the described data set. The entries in the data set cannot all be the same. Mean, median, and mode are the same.

Graphical Analysis In Exercises 9 –12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Graphical Analysis In Exercises 9 –12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision. The frequency distribution of 180 rolls of a dodecagon (a 12-sided die)

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision. The frequency distribution of scores on a 90-point test where a few students scored much lower than the majority of students

Problem 17E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. College Credits The numbers of credits being taken by a sample of 13 full-time college students for a semester 12 14 16 15 13 14 15 18 16 16 12 16 15

Graphical Analysis In Exercises 9 –12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision. The frequency distribution of salaries at a company where a few executives make much higher salaries than the majority of employees

Problem 18E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. LSAT Scores The Law School Admission Test (LSAT) scores for a sample of seven students accepted into a law school 174 172 169 176 169 170 175

Graphical Analysis In Exercises 9 –12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Problem 19E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Journalism The lengths (in words) of seven articles from The New York Times (Source: The New York Times) 1125 1277 1275 1370 1155 1229 818

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision. The frequency distribution of weights for a sample of seventh-grade boys

Problem 21E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Tuition The 2012-2013 tuition and fees (in thousands of dollars) for the top 14 universities (Source: U.S. News&World Report) 41 39 42 47 45 42 42 44 44 40 45 44 44 44

Problem 20E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Representatives The ages of the members of the House of Representatives from Indiana as of February 19, 2013 (Source: Library of Congress) 63 49 36 43 52 43 38 50 40

Problem 23E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. NFL The numbers of points scored by the Denver Broncos during the 2012 regular season (Source: National Football League) 31 21 25 37 21 35 34 31 36 30 17 31 26 34 34 38

Problem 24E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Power Failures The durations (in minutes) of power failures at a residence in the last 10 years 18 26 45 75 125 80 33 40 44 49 89 80 96 125 12 61 31 63 103 28

Problem 25E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Eating Disorders The numbers of weeks it took to reach a target weight for a sample of five patients with eating disorders treated by psychodynamic psychotherapy (Source: The Journal of Consulting and Clinical Psychology) 15.0 31.5 10.0 25.5 1.0

Problem 22E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Cholesterol The cholesterol levels of a sample of 10 female employees 154 240 171 188 235 203 184 173 181 275

Problem 26E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Eating Disorders The numbers of weeks it took to reach a target weight for a sample of 14 patients with eating disorders treated by psychodynamic psychotherapy and cognitive behavior techniques (Source: The Journal of Consulting and Clinical Psychology) 2.5 20.0 11.0 10.5 17.5 16.5 13.0 15.5 26.5 2.5 27.0 28.5 1.5 5.0

Problem 27E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Eyeglasses and Contacts The responses of a sample of 1000 adults who were asked what type of corrective lenses they wore are shown in the table at the left. (Adapted from American Optometric Association) Type of lenses Frequency, f Contacts Eyeglasses Contacts and eyeglasses None 40 570 180 210

Problem 28E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Living on Your Own The responses of a sample of 1177 young adults who were asked what surprised them the most as they began to live on their own (Adapted from Charles Schwab) Amount of first salary: 63 Trying to find a job: 125 Number of decisions: 163 Money needed: 326 Paying bills: 150 Trying to save: 275 How hard it is breaking away from parents: 75

Problem 29E Finding and Discussing the Mean, Median, and Mode In Exercise, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Class Level The class levels of 25 students in a physics course Freshman: 2 Sophomore: 5 Junior: 10 Senior: 8

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Facebook The pie chart at the left shows the responses of a sample of 614 small-business owners who were asked about their presence on Facebook. (Adapted from Manta)

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Grade Point Averages of Students in a Class

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Weights (in pounds) of Carry-On Luggage on a Plane

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Prices (in dollars per night) of Hotel Rooms in a City

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Times (in minutes) It Takes Employees to Drive to Work

Problem 35E Graphical Analysis In Exercise, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers. Sick Days Used by Employees

Graphical Analysis In Exercises 35 and 36, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers. Hourly Wages of Employees

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Do You Send Thank-You Notes After a Job Interview? (Adapted from TheLadders)

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Heights of Players on Two Opposing Volleyball Teams

Problem 41E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Final Grade The scores and their percents of the final grade for a statistics student are shown below. What is the student’s mean score? Score Percent of final grade Homework 85 5% Quizzes 80 35% Project 100 20% Speech 90 15% Final exam 93 25%

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Heart Rates of a Sample of Adults

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Body Mass Indexes (BMI) of People in a Gym

Problem 42E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Final Grade The scores and their percents of the final grade for an archaeology student are shown below. What is the student’s mean score? Score Percent of final grade Article reviews 95 10% Quizzes 100 10% Midterm exam 89 30% Student lecture 100 10% Final exam 92 40%

Problem 43E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Account Balance For the month of April, a checking account has a balance of $523 for 24 days, $2415 for 2 days, and $250 for 4 days. What is the account’s mean daily balance for April?

Problem 44E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Finding the Weighted Mean In Exercise, find the weighted mean of the data. Account Balance For the month of May, a checking account has a balance of $759 for 15 days, $1985 for 5 days, $l4l0 for 5 days, and $348 for 6 days. What is the account’s mean daily balance for May?

Problem 47E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Final Grade In Exercise, an error was made in grading your final exam. Instead of getting 93, you scored 85. What is your new weighted mean? In Exercise, find the weighted mean of the data. The scores and their percents of the final grade for a statistics student are shown below. What is the student’s mean score? Score Percent of final grade Homework 85 5% Quizzes 80 35% Project 100 20% Speech 90 15% Final exam 93 25%

Problem 48E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Grades In Exercise, one of the student’s B grades gets changed to an A. What is the student’s new mean grade point score? In Exercise, find the weighted mean of the data. Grades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student’s mean grade point score? A in 1 four-credit class B in 2 three-credit classes C in 1 three-credit class D in 1 two-credit class

Problem 49E Finding the Mean of a Frequency DistributionIn Exercise, approximate the mean of the frequency distribution. Fuel Economy The highway mileage (in miles per gallon) for Mileage (in miles per gallon) Frequency 29 – 33 11 34 –38 12 39 – 43 2 44 – 48 5

Problem 45E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Grades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student’s mean grade point score? A in 1 four-credit class B in 2 three-credit classes C in 1 three-credit class D in 1 two-credit class

Problem 50E Finding the Mean of a Frequency Distribution In Exercise, approximate the mean of the frequency distribution. Fuel Economy The city mileage (in miles per gallon) for 24 family sedans Mileage (in miles per gallon) Frequency 22 – 27 16 28 –33 2 34 – 39 2 40 – 45 3 46 – 51 1

Problem 51E Finding the Mean of a Frequency Distribution In Exercise, approximate the mean of the frequency distribution Ages The ages of the residents of Medicine Lake, Montana, in 2010 (Source: U.S. Census Bureau) Age Frequency 0 – 9 44 10 –19 66 20 –29 32 30 –39 53 40 – 49 35 50 – 59 31 60 – 69 23 70 –79 13 80 – 89 2

Problem 52E Finding the Mean of a Frequency Distribution In Exercise, approximate the mean of the frequency distribution Ages The ages of the residents of Medicine Lake, Montana, in 2010 (Source: U.S. Census Bureau) Age Frequency 0 – 9 30 10 –19 28 20 –29 17 30 –39 22 40 – 49 23 50 – 59 46 60 – 69 37 70 –79 18 80 – 89 4

Problem 46E Finding the Weighted Mean In Exercise, find the weighted mean of the data. Scores The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 85 5 math majors: 90 13 business majors: 81

Problem 53E Identifying the Shape of a Distribution In Exercise, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Hospital Beds Number of classes: 5 Data set: The number of beds in a sample of 24 hospitals 149 167 162 127 130 180 160 167 221 145 137 194 207 150 254 262 244 297 137 204 166 174 180 151

Problem 54E Identifying the Shape of a Distribution In Exercise, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Hospitalization Number of classes: 6 Data set: The number of days 20 patients remained hospitalized 6 9 7 14 4 5 6 8 4 11 10 6 8 6 5 7 6 6 3 11

Problem 55E Identifying the Shape of a Distribution In Exercise, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Heights of Males Number of classes: 5 Data set: The heights (to the nearest inch) of 30 males 67 76 69 68 72 68 65 63 75 69 66 72 67 66 69 73 64 62 71 73 68 72 71 65 69 66 74 72 68 69

Problem 56E Identifying the Shape of a Distribution In Exercise, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. Six-Sided Die Number of classes: 6 Data set: The results of rolling a six-sided die 30 times 1 4 6 1 5 3 2 5 4 6 1 2 4 3 5 6 3 2 1 1 5 6 2 4 4 3 1 6 2 4

Problem 57E Coffee Contents During a quality assurance check, the actual coffe contents (in ounces) of six jars of instant coffee were recorded as 6.03, 5.59, 6.40, 6.00, 5.99, and 6.02. (a) Find the mean and the median of the coffee content. ________________ (b) The third value was incorrectly measured and is actually 6.04. Find the mean and the median of the coffee content again. ________________ (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?

Problem 58E U.S. Exports The table at the left shows the U.S. exports (in billions of dollars) to 19 countries for a recent year. (Source: U.S. Department of Commerce) (a) Find the mean and the median of the exports. ________________ (b) Find the mean and the median without the U.S. exports to Canada. Which measure of central tendency, the mean or the median, was affected more by the elimination of the Canadian exports? ________________ (c) The U.S. exports to India were $21.5 billion. Find the mean and the median with the Indian exports added to the original data set. Which measure of central tendency was affected more by adding the Indian exports? U.S. exports (in billions of dollars) Canada: 280.9 Japan: 65.7 Mexico: 198.4 South Korea: 43.4 Germany: 49.2 Singapore: 31.2 Taiwan: 25.9 France: 27.8 Netherlands: 42.4 Brazil: 42.9 China: 103.9 Belgium: 29.9 Australia: 27.5 Italy: 16.0 Malaysia: 14.2 Thailand: 10.9 Switzerland: 24.4 Saudi Arabia: 13.8 United Kingdom: 55.9

Graphical Analysis In Exercises 59 and 60, identify any clusters, gaps, or outliers. 2013 Most Fuel Efficient Vehicles* (Source: United States Environmental Protection Agency)

Graphical Analysis In Exercises 59 and 60, identify any clusters, gaps, or outliers. 2013 Most Fuel Efficient Trucks, Vans, and SUVs (Source: United States Environmental Protection Agency)

Writing Consider the data set given in Exercise 59. Which of the options below do you think is better for representing the data? Explain your reasoning. Option 1: reporting the mean of all of the vehicles Option 2: treating cars as one data set, treating trucks, vans, and SUVs as a second data set, and reporting the mean of each data set

Problem 62EC Golf The distances (in yards) for nine holes of a golf course are listed. 336 393 408 522 147 504 177 375 360 (a) Find the mean and the median of the data. ________________ (b) Convert the distances to feet. Then rework part (a). ________________ (c) Compare the measures you found in part (b) with those found in part (a). What do you notice? ________________ (d) Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.

Problem 63EC Data Analysis A consumer testing service obtained the mileages (in miles per gallon) shown in the table at the left in five test runs performed with three types of compact cars. (a) The manufacturer of Car A wants to advertise that its car performed best in this test. Which measure of central tendency-mean, median, or mode—should be used for its claim? Explain your reasoning. ________________ (b) The manufacturer of Car B wants to advertise that its car performed best in this test. Which measure of central tendency—mean, median, or mode—should be used for its claim? Explain your reasoning. ________________ (c) The manufacturer of Car C wants to advertise that its car performed best in this test. Which measure of central tendency—mean, median, or mode—should be used for its claim? Explain your reasoning. Car A B C Run 1 28 31 29 Run 2 32 29 32 Run 3 28 31 28 Run 4 30 29 32 Run 5 34 31 30

True or False? In Exercises 1 4, determine whether the statement is true or false. If it is false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.

True or False? In Exercises 1 4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.. Some quantitative data sets do not have medians.

True or False? In Exercises 1 4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.A data set can have the same mean, median, and mode

`True or False? In Exercises 1 4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.When each data class has the same frequency, the distribution is symmetric.

Constructing Data Sets In Exercises 58, construct the described data set. The entries in the data set cannot all be the same.Median and mode are the same.

Constructing Data Sets In Exercises 58, construct the described data set. The entries in the data set cannot all be the same.Mean and mode are the same.

Constructing Data Sets In Exercises 58, construct the described data set. The entries in the data set cannot all be the same.. Mean is not representative of a typical number in the data set.

Constructing Data Sets In Exercises 58, construct the described data set. The entries in the data set cannot all be the same.Mean, median, and mode are the same.

Graphical Analysis In Exercises 912, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Graphical Analysis In Exercises 912, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Graphical Analysis In Exercises 912, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Graphical Analysis In Exercises 912, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Matching In Exercises 1316, match the distribution with one of the graphs in Exercises 912. Justify your decision. The frequency distribution of 180 rolls of a dodecagon (a 12-sided die)

Matching In Exercises 1316, match the distribution with one of the graphs in Exercises 912. Justify your decision.The frequency distribution of salaries at a company where a few executives make much higher salaries than the majority of employees

Matching In Exercises 1316, match the distribution with one of the graphs in Exercises 912. Justify your decision.The frequency distribution of scores on a 90-point test where a few students scored much lower than the majority of students

Matching In Exercises 1316, match the distribution with one of the graphs in Exercises 912. Justify your decision.The frequency distribution of weights for a sample of seventh-grade boys

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyCollege Credits The numbers of credits being taken by a sample of 13 full-time college students for a semester 12 14 16 15 13 14 15 18 16 16 12 16 15

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyLSAT Scores The Law School Admission Test (LSAT) scores for a sample of seven students accepted into a law school 174 172 169 176 169 170 175

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why Journalism The lengths (in words) of seven articles from The New York Times (Source: The New York Times) 1125 1277 1275 1370 1155 1229 818

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyRepresentatives The ages of the members of the House of Representatives from Indiana as of February 19, 2013 (Source: Library of Congress) 63 49 36 43 52 43 38 50 40

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Tuition The 20122013 tuition and fees (in thousands of dollars) for the top 14 universities (Source: U.S. News & World Report) 41 39 42 47 45 42 42 44 44 40 45 44 44 44

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Cholesterol The cholesterol levels of a sample of 10 female employees 154 240 171 188 235 203 184 173 181 275

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"NFL The numbers of points scored by the Denver Broncos during the 2012 regular season (Source: National Football League) 31 21 25 37 21 35 34 31 36 30 17 31 26 34 34 38

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyPower Failures The durations (in minutes) of power failures at a residence in the last 10 years 18 26 45 75 125 80 33 40 44 49 89 80 96 125 12 61 31 63 103 28

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Eating Disorders The numbers of weeks it took to reach a target weight for a sample of five patients with eating disorders treated by psychodynamic psychotherapy (Source: The Journal of Consulting and Clinical Psychology) 15.0 31.5 10.0 25.5 1.0

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyEating Disorders The numbers of weeks it took to reach a target weight for a sample of 14 patients with eating disorders treated by psychodynamic psychotherapy and cognitive behavior techniques (Source: The Journal of Consulting and Clinical Psychology) 2.5 20.0 11.0 10.5 17.5 16.5 13.0 15.5 26.5 2.5 27.0 28.5 1.5 5.0

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Eyeglasses and Contacts The responses of a sample of 1000 adults who were asked what type of corrective lenses they wore are shown in the table at the left. (Adapted from American Optometric Association)

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyLiving on Your Own The responses of a sample of 1177 young adults who were asked what surprised them the most as they began to live on their own (Adapted from Charles Schwab) Amount of first salary: 63 Trying to find a job: 125 Number of decisions: 163 Money needed: 326 Paying bills: 150 Trying to save: 275 How hard it is breaking away from parents: 75

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Class Level The class levels of 25 students in a physics course Freshman: 2 Junior: 10 Sophomore: 5 Senior: 8

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Facebook The pie chart at the left shows the responses of a sample of 614 small-business owners who were asked about their presence on Facebook. (Adapted from Manta)

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Weights (in pounds) of Carry-On Luggage on a Plane 0 6 7 Key: 3 0 2 = 32 1 2 5 8 9 2 0 4 4 4 5 8 9 3 2 2 3 5 5 5 6 8 9 4 0 1 2 7 8 5 1

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Grade Point Averages of Students in a Class 0 8 Key: 0 0 8 = 0.8 1 5 6 8 2 1 3 4 5 3 0 9 4 0 0

"Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why"Times (in minutes) It Takes Employees to Drive to Work

Finding and Discussing the Mean, Median, and Mode In Exercises 1734, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain whyPrices (in dollars per night) of Hotel Rooms in a City

Graphical Analysis In Exercises 35 and 36, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers Sick Days Used by Employees

Graphical Analysis In Exercises 35 and 36, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers Hourly Wages of Employees

In Exercises 37 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.Do You Send Thank-You Notes After a Job Interview?

In Exercises 37 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.Heights of Players on Two Opposing Volleyball Teams

In Exercises 37 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.Heart Rates of a Sample of Adults

In Exercises 37 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.Body Mass Indexes (BMI) of People in a Gym

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the dataFinal Grade The scores and their percents of the final grade for a statistics student are shown below. What is the students mean score? Score Percent of final grade Homework 85 5% Quizzes 80 35% Project 100 20% Speech 90 15% Final exam 93 25%

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the dataFinal Grade The scores and their percents of the final grade for an archaeology student are shown below. What is the students mean score? Score Percent of final grade Article reviews 95 10% Quizzes 100 10% Midterm exam 89 30% Student lecture 100 10% Final exam 92 40%

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the data Account Balance For the month of April, a checking account has a balance of $523 for 24 days, $2415 for 2 days, and $250 for 4 days. What is the accounts mean daily balance for April?

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the dataAccount Balance For the month of May, a checking account has a balance of $759 for 15 days, $1985 for 5 days, $1410 for 5 days, and $348 for 6 days. What is the accounts mean daily balance for May?

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the dataGrades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the students mean grade point score? A in 1 four-credit class C in 1 three-credit class B in 2 three-credit classes D in 1 two-credit class

Finding the Weighted Mean In Exercises 41 46, find the weighted mean of the data.Scores The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 85 5 math majors: 90 13 business majors: 81

. Final Grade In Exercise 41, an error was made in grading your final exam. Instead of getting 93, you scored 85. What is your new weighted mean?

Grades In Exercise 45, one of the students B grades gets changed to an A. What is the students new mean grade point score?

Finding the Mean of a Frequency Distribution In Exercises 4952, approximate the mean of the frequency distribution. Fuel Economy The highway mileage (in miles per gallon) for 30 small cars Mileage (in miles per gallon) Frequency 29 33 11 3438 12 39 43 2 4448 5

Finding the Mean of a Frequency Distribution In Exercises 4952, approximate the mean of the frequency distribution. Fuel Economy The city mileage (in miles per gallon) for 24 family sedans Mileage (in miles per gallon) Frequency 2227 16 2833 2 3439 2 4045 3 4651 1

Finding the Mean of a Frequency Distribution In Exercises 4952, approximate the mean of the frequency distribution. Ages The ages of the residents of Tse Bonito, New Mexico, in 2010 (Source: U.S. Census Bureau) Age Frequency 09 44 1019 66 2029 32 3039 53 40 49 35 5059 31 6069 23 7079 13 8089 2

Finding the Mean of a Frequency Distribution In Exercises 4952, approximate the mean of the frequency distribution. Ages The ages of the residents of Medicine Lake, Montana, in 2010 (Source: U.S. Census Bureau) Age Frequency 0 9 30 1019 28 2029 17 3039 22 4049 23 5059 46 6069 37 7079 18 8089 4

Identifying the Shape of a Distribution In Exercises 5356, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.Hospital Beds Number of classes: 5 Data set: The number of beds in a sample of 24 hospitals 149 167 162 127 130 180 160 167 221 145 137 194 207 150 254 262 244 297 137 204 166 174 180 151

Identifying the Shape of a Distribution In Exercises 5356, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.Hospitalization Number of classes: 6 Data set: The number of days 20 patients remained hospitalized 6 9 7 14 4 5 6 8 4 11 10 6 8 6 5 7 6 6 3 11

Identifying the Shape of a Distribution In Exercises 5356, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.Heights of Males Number of classes: 5 Data set: The heights (to the nearest inch) of 30 males 67 76 69 68 72 68 65 63 75 69 66 72 67 66 69 73 64 62 71 73 68 72 71 65 69 66 74 72 68 69

Identifying the Shape of a Distribution In Exercises 5356, construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these.Six-Sided Die Number of classes: 6 Data set: The results of rolling a six-sided die 30 times 1 4 6 1 5 3 2 5 4 6 1 2 4 3 5 6 3 2 1 1 5 6 2 4 4 3 1 6 2 4

Coffee Contents During a quality assurance check, the actual coffee contents (in ounces) of six jars of instant coffee were recorded as 6.03, 5.59, 6.40, 6.00, 5.99, and 6.02. (a) Find the mean and the median of the coffee content. (b) The third value was incorrectly measured and is actually 6.04. Find the mean and the median of the coffee content again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?

. U.S. Exports The table at the left shows the U.S. exports (in billions of dollars) to 19 countries for a recent year. (Source: U.S. Department of Commerce) (a) Find the mean and the median of the exports. (b) Find the mean and the median without the U.S. exports to Canada. Which measure of central tendency, the mean or the median, was affected more by the elimination of the Canadian exports? (c) The U.S. exports to India were $21.5 billion. Find the mean and the median with the Indian exports added to the original data set. Which measure of central tendency was affected more by adding the Indian exports?

Graphical Analysis In Exercises 59 and 60, identify any clusters, gaps, or outliers. 2013 Most Fuel Efcient Vehicles*

Graphical Analysis In Exercises 59 and 60, identify any clusters, gaps, or outliers. 2013 Most Fuel Efcient Trucks, Vans, and SUVs

Writing Consider the data set given in Exercise 59. Which of the options below do you think is better for representing the data? Explain your reasoning. Option 1: reporting the mean of all of the vehicles Option 2: treating cars as one data set, treating trucks, vans, and SUVs as a second data set, and reporting the mean of each data set

Golf The distances (in yards) for nine holes of a golf course are listed. 336 393 408 522 147 504 177 375 360 (a) Find the mean and the median of the data. (b) Convert the distances to feet. Then rework part (a). (c) Compare the measures you found in part (b) with those found in part (a). What do you notice? (d) Use your results from part (c) to explain how to quickly find the mean and the median of the original data set when the distances are converted to inches.

Data Analysis A consumer testing service obtained the mileages (in miles per gallon) shown in the table at the left in five test runs performed with three types of compact cars. (a) The manufacturer of Car A wants to advertise that its car performed best in this test. Which measure of central tendencymean, median, or modeshould be used for its claim? Explain your reasoning. (b) The manufacturer of Car B wants to advertise that its car performed best in this test. Which measure of central tendencymean, median, or modeshould be used for its claim? Explain your reasoning. (c) The manufacturer of Car C wants to advertise that its car performed best in this test. Which measure of central tendencymean, median, or modeshould be used for its claim? Explain your reasoning

Midrange Another measure of central tendency that is rarely used but is easy to calculate is the midrange. It can be found by using the formula Midrange = 1Maximum data entry2 + 1Minimum data entry2 2 . Which of the manufacturers in Exercise 63 would prefer to use the midrange statistic in their ads? Explain your reasoning.

Data Analysis Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown in the table at the left. (a) Find the mean and the median of the data. (b) Draw a stem-and-leaf plot for the data using one row per stem. Locate the mean and the median on the display. (c) Describe the shape of the distribution.

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries. (a) Find the 10% trimmed mean for the data in Exercise 65. (b) Compare the four measures of central tendency, including the midrange. (c) What is the benefit of using a trimmed mean versus using a mean found using all data entries? Explain your reasoning.