Solution: Finding the Mean of a Frequency Distribution In

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 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 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 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.

Problem 9E Graphical Analysis In Exercise, 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 10E Graphical Analysis In Exercise, 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 11E Graphical Analysis In Exercise, 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 12E Graphical Analysis In Exercise, 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 13E Matching In Exercise, match the distribution with one of the graphs in Exercises. Justify your decision. The frequency distribution of 180 rolls of a dodecagon (a 12-sided die) Exercises (a) (b) (c) (d)

Problem 14E Matching In Exercise, match the distribution with one of the graphs in Exercises. Justify your decision. The frequency distribution of salaries at a company where a few executives make much higher salaries than the majority of employees Exercises (a) (b) (c) (d)

Problem 15E Matching In Exercise, match the distribution with one of the graphs in Exercises. 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 Exercises (a) (b) (c) (d)

Problem 16E Matching In Exercise, match the distribution with one of the graphs in Exercises. Justify your decision. The frequency distribution of weights for a sample of seventh-grade boys Exercises (a) (b) (c) (d)

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. Cholesterol The cholesterol levels of a sample of 10 female employees 154 240 171 188 235 203 184 173 181 275

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. 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 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. 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 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. 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 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. 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 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. 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 31E 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. Weights (in pounds) of Carry-On Luggage on a Plane

Problem 32E 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. Grade Point Averages of Students in a Class

Problem 33E 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. Times (in minutes) It Takes Employees to Drive to Work

Problem 34E 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. Prices (in dollars per night) of Hotel Rooms in a City

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

Problem 38E In Exercises 38, 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 36E 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. Hourly Wages of Employees

Problem 39E In Exercises 39, 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

Problem 40E In Exercises 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 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%

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 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 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 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 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 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

Problem 61E 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 62E 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

Problem 63E 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 Which of the manufacturers In Exercise, would prefer to use the midrange statistic in their ads? Explain your reasoning.

Problem 64E 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. Test scores 44 51 11 90 76 36 64 37 43 72 53 62 36 74 51 72 37 28 38 61 47 63 36 41 22 37 51 46 85 13

Problem 65E 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,. ________________ (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.