Describe the shape of the distribution for the histogram

Problem 1CQ The data set represents the numbers of minutes a sample of 25 people exercise each week. 108 139 120 123 120 132 123 131 131 157 150 124 111 101 135 119 116 117 127 128 139 119 118 114 127 (a) Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. ________________ (b) Display the data using a frequency histogram and a frequency polygon on the same axes. ________________ (c) Display the data using a relative frequency histogram. ________________ (d) Describe the shape of the distribution as symmetric, uniform, or skewed left, skewed right, or none of these. ________________ (e) Display the data using a stem-and-leaf plot. Use one line per stem. ________________ (f) Display the data using a box-and-whisker plot. ________________ (g) Display the data using an ogive.

Problem 1CR In Exercise, identify the sampling technique used, and discuss potential sources of bias (if any). Explain. For quality assurance, every fortieth toothbrush is taken from each of four assembly lines and tested to make sure the bristles stay in the toothbrush.

Problem 1E In Exercises 1, use the data set, which represents the student-to-faculty ratios for 20 public colleges. (Source: Kiplinger) 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 20 15 Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Problem 2CQ Use frequency distribution formulas to approximate the sample mean and the sample standard deviation of the data set in Exercise 1. The data set represents the numbers of minutes a sample of 25 people exercise each week. 108 139 120 123 120 132 123 131 131 157 150 124 111 101 135 119 116 117 127 128 139 119 118 114 127 (a) Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. ________________ (b) Display the data using a frequency histogram and a frequency polygon on the same axes. ________________ (c) Display the data using a relative frequency histogram. ________________ (d) Describe the shape of the distribution as symmetric, uniform, or skewed left, skewed right, or none of these. ________________ (e) Display the data using a stem-and-leaf plot. Use one line per stem. ________________ (f) Display the data using a box-and-whisker plot. ________________ (g) Display the data using an ogive.

Problem 1PTE How Would You Do It? (a) How would you investigate the complaints from renters who are unhappy about their monthly rents? ________________ (b) Which statistical measure do you think would best represent the data sets for the four areas of the city? ________________ (c) Calculate the measure from part (b) for each of the four areas.

Problem 2CR In Exercise, identify the sampling technique used, and discuss potentialsources of bias (if any). Explain. Using random digit dialing, researchers asked 1200 U.S. adults their thoughts on health care reform.

Problem 2E In Exercise, use the data set, which represents the student-to-faculty ratios for 20 public colleges. (Source: Kiplinger) 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 20 15 Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency. In Exercises, use the data set, which represents the student-to-faculty ratios for 20 public colleges. (Source: Kiplinger) 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 20 15 Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Problem 2PTE Displaying the Data (a) What type of graph would you choose to display the data? Explain your reasoning. ________________ (b) Construct the graph from part (a). ________________ (c) Based on your data displays, does it appear that the monthly rents in Area A are higher than the rents in the other areas of the city? Explain.

Problem 3E In Exercise, use the data set shown in the table at the left, which represents the actual liquid volumes (in ounces) in 24 twelve-ounce cans. Construct a frequency histogram for the data set using seven classes. Volumes (in ounces) 11.95 11.91 11.86 11.94 12.00 11.93 12.00 11.94 12.10 11.95 11.99 11.94 11.89 12.01 11.99 11.94 11.92 11.98 11.88 11.94 11.98 11.92 11.95 11.93

Problem 3PTE Measuring the Data (a) What other statistical measures in this chapter could you use to analyze the monthly rent data? ________________ (b) Calculate the measures from part (a). ________________ (c) Compare the measures from part (b) with the graph you constructed in Exercise. Do the measurements support your conclusion in Exercise? Explain. Exercise Displaying the Data (a) What type of graph would you choose to display the data? Explain your reasoning. ________________ (b) Construct the graph from part (a). ________________ (c) Based on your data displays, does it appear that the monthly rents in Area A are higher than the rents in the other areas of the city? Explain.

Problem 4E In Exercise, use the data set shown in the table at the left, which represents the actual liquid volumes (in ounces) in 24 twelve-ounce cans. Construct a relative frequency histogram for the data set using seven classes. Volumes (in ounces) 11.95 11.91 11.86 11.94 12.00 11.93 12.00 11.94 12.10 11.95 11.99 11.94 11.89 12.01 11.99 11.94 11.92 11.98 11.88 11.94 11.98 11.92 11.95 11.93

Problem 4PTE Discussing the Data (a) Do you think the complaints in Area A are legitimate? How do you think they should be addressed? ________________ (b) What reasons might you give as to why the rents vary among different areas of the city?

Problem 5CQ Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. The data set has a bell-shaped distribution. Using the Empirical Rule, between what two prices do 95% of the houses fall?

Problem 5E In Exercise, use the data set, which represents the numbers of rooms reserved during one night’s business at a sample of hotels. 153 104 118 166 89 104 100 79 93 96 116 94 140 84 81 96 108 111 87 126 101 111 122 108 126 93 108 87 103 95 129 93 Construct a frequency distribution for the data set with six classes and draw a frequency polygon.

Problem 6CQ Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. Refer to the sample statistics from Exercise 5 and use z-scores to determine whether any of the following house prices are unusual. (a) $200,000 (b) $55,000 (c) $175,000 (d) $122,000 Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. The data set has a bell-shaped distribution. Using the Empirical Rule, between what two prices do 95% of the houses fall?

Problem 6CR The mean annual salary for a sample of electrical engineers is $83,500, with a standard deviation of $1500. The data set has a bell-shaped distribution. (a) Use the Empirical Rule to estimate the percent of electrical engineers whose annual salaries are between $80,500 and $86,500. ________________ (b) In a sample of 40 additional electrical engineers, about how many electrical engineers would you expect to have annual salaries between $80,500 and $86,500? ________________ (c) The salaries of three randomly selected electrical engineers are $90,500, $79,750, and $82,600. Find the z-score that corresponds to each salary. Determine whether any of these salaries are unusual.

Problem 6E In Exercise, use the data set, which represents the numbers of rooms reserved during one night’s business at a sample of hotels. 153 104 118 166 89 104 100 79 93 96 116 94 140 84 81 96 108 111 87 126 101 111 122 108 126 93 108 87 103 95 129 93 Construct an ogive for the data set using six classes.

Problem 7E In Exercise, use the data set, which represents the air quality indices for 30 U.S. cities. (Source: AIRNow) 25 35 20 75 10 10 61 89 44 22 34 33 38 30 47 53 44 57 71 20 42 52 48 41 35 59 53 61 65 25 Use a stem-and-leaf plot to display the data set. Describe any patterns.

Problem 8E In Exercise, use the data set, which represents the air quality indices for 30 U.S. cities. (Source: AIRNow) 25 35 20 75 10 10 61 89 44 22 34 33 38 30 47 53 44 57 71 20 42 52 48 41 35 59 53 61 65 25 Use a dot plot to display the data set. Describe any patterns.

Problem 9E The heights (in feet) and the numbers of stories of nine buildings in Houston are listed. Use a scatter plot to display the data. Describe any patterns. (Source: Emporis Corporation) Height (in feet) 992 780 762 756 741 732 714 662 579 Number of stories 71 56 53 55 47 53 50 49 40

Problem 11E In Exercise, use the data set, which represents the results of a survey that asked U.S. adults where they would be at midnight when the new year arrived. (Adapted from Rasmussen Reports) Response At home At friend’s home At restaurant or bar Somewhere else Not sure Number 620 110 50 100 130 Use a pie chart to display the data set. Describe any patterns.

Problem 12E In Exercise, use the data set, which represents the results of a survey that asked U.S. adults where they would be at midnight when the new year arrived. (Adapted from Rasmussen Reports) Response At home At friend’s home At restaurant or bar Somewhere else Not sure Number 620 110 50 100 130 Use a Pareto chart to display the data set. Describe any patterns.

Problem 14CR Five test scores are shown below. The first 4 test scores are 15% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores. 85 92 84 89 91

Problem 15CR Tail lengths (in feet) for a sample of American alligators are listed. 6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6 (a) Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning. ________________ (b) Find the range, variance, and standard deviation of the data set.

Problem 15E Estimate the mean of the frequency distribution you made in Exercise 1. In Exercises, use the data set, which represents the student-to-faculty ratios for 20 public colleges. (Source: Kiplinger) 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 20 15 Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Problem 16CR A study shows that the number of deaths due to heart disease for women has decreased every year for the past five years. (a) Make an inference based on the results of the study. ________________ (b) What is wrong with this type of reasoning?

Problem 17E Six test scores are shown below. The first 5 test scores are 15% of the final grade, and the last test score is 25% of the final grade. Find the weighted mean of the test scores. 78 72 86 91 87 80

Problem 18E Four test scores are shown below. The first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores. 96 85 91 86

Problem 19E Describe the shape of the distribution for the histogram you made in Exercise 3 as symmetric, uniform, skewed left, skewed right, or none of these. In Exercise, use the data set shown in the table at the left, which represents the actual liquid volumes (in ounces) in 24 twelve-ounce cans. Construct a frequency histogram for the data set using seven classes. Volumes (in ounces) 11.95 11.91 11.86 11.94 12.00 11.93 12 11.94 12.10 11.95 11.99 11.94 11.89 12.01 11.99 11.94 11.92 11.98 11.88 11.94 11.98 11.92 11.95 11.93

Problem 20E Describe the shape of the distribution for the histogram you made in Exercise 4 as symmetric, uniform, skewed left, skewed right, or none of these. In Exercise, use the data set shown in the table at the left, which represents the actual liquid volumes (in ounces) in 24 twelve-ounce cans. Construct a relative frequency histogram for the data set using seven classes. Volumes (in ounces) 11.95 11.91 11.86 11.94 12.00 11.93 12.00 11.94 12.10 11.95 11.99 11.94 11.89 12.01 11.99 11.94 11.92 11.98 11.88 11.94 11.98 11.92 11.95 11.93

Problem 21E In Exercise, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Problem 22E In Exercise, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Problem 23E For the histogram In Exercise, which is greater, the mean or the median? Explain your reasoning. In Exercise, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Problem 24E For the histogram In Exercise, which is greater, the mean or the median? Explain your reasoning. In Exercise, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Problem 27E In Exercise, find the range, mean, variance, and standard deviation of the population data set. The mileages (in thousands of miles) for a rental car company’s fleet. 4 2 9 12 15 3 6 8 1 4 14 12 3 3

Problem 30E In Exercise, find the range, mean, variance, and standard deviation of the sample data set. Salaries (in dollars) of a random sample of high school teachers 49,632 54,619 58,298 48,250 51,842 50,875 53,219 49,924

Problem 35E From a random sample of households, the numbers of televisions are listed. Find the sample mean and the sample standard deviation of the data. Number of televisions 0 1 2 3 4 5 Number of households 1 8 13 10 5 3

Problem 36E From a random sample of airplanes, the numbers of defects found in their fuselages are listed. Find the sample mean and the sample standard deviation of the data. Number of defects 0 1 2 3 4 5 6 Number of airplanes 4 5 2 9 1 3 1

Problem 37E In Exercise, use the data set, which represents the fuel economies (in highway miles per gallon) of several Harley-Davidson motorcycles. (Source: Total Motorcycle) 53 57 60 57 54 53 54 53 54 42 48 53 47 47 50 48 42 42 54 54 60 Find the five-number summary of the data set.

Problem 38E In Exercise, use the data set, which represents the fuel economies (in highway miles per gallon) of several Harley-Davidson motorcycles. (Source: Total Motorcycle) 53 57 60 57 54 53 54 53 54 42 48 53 47 47 50 48 42 42 54 54 60 Find the interquartile range of the data set.

Problem 39E In Exercise, use the data set, which represents the fuel economies (in highway miles per gallon) of several Harley-Davidson motorcycles. (Source: Total Motorcycle) 53 57 60 57 54 53 54 53 54 42 48 53 47 47 50 48 42 42 54 54 60 Draw a box-and-whisker plot that represents the data set.

Problem 40E In Exercise, use the data set, which represents the fuel economies (in highway miles per gallon) of several Harley-Davidson motorcycles. (Source: Total Motorcycle) 53 57 60 57 54 53 54 53 54 42 48 53 47 47 50 48 42 42 54 54 60 About how many motorcycles fall on or below the third quartile?

Problem 41E Find the interquartile range of the data set from Exercise 13. 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. The vertical jumps (in inches) of a sample of 10 college basketball players at the 2012 NBA Draft Combine (Source: DraftExpress) 24.5 29.5 32.5 28.0 28.5 25.5 34.0 24.5 30.0 31.0

Problem 42E The weights (in pounds) of the defensive players on a high school football team are shown below. Draw a box-and-whisker plot that represents the data set and describe the shape of the distribution. 173 145 205 192 197 227 156 240 172 185 208 185 190 167 212 228 190 184 195

Problem 43E A student’s test grade of 75 represents the 65th percentile of the grades. What percent of students scored higher than 75?

Problem 45E The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercise, (a) transform the towing capacity to a z-score, (b) interpret the results, and (c) determine whether the towing capacity is unusual. 16,500 pounds

Problem 46E The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercise, (a) transform the towing capacity to a z-score, (b) interpret the results, and (c) determine whether the towing capacity is unusual. 5500 pounds

Problem 47E The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercise, (a) transform the towing capacity to a z-score, (b) interpret the results, and (c) determine whether the towing capacity is unusual. 18,000 pounds

Problem 48E The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercise, (a) transform the towing capacity to a z-score, (b) interpret the results, and (c) determine whether the towing capacity is unusual. 11,300 pounds