Data on x poverty rate (%) and y high school dropout rate

The Chronicle of Higher Education (August 31, 2001) published data collected in a survey of a large number of students who were college freshmen in the fall of 2001. Of those surveyed, 70.6% reported that they were attending their first-choice college, 20.8% their secondchoice college, 5.5% their third-choice college, and 3.1% their fourth- or higher-choice college. Use a pie chart to display this information.

The article Rinse Out Your Mouth (Associated Press, March 29, 2006) summarized results from a survey of 1001 adults on the use of profanity. When asked How many times do you use swear words in conversations? 46% responded a few or more times per week, 32% responded a few times a month or less, and 21% responded never. Use the given information to construct a segmented bar chart.

Data from the U.S Census Bureau was used to construct the accompanying pie chart that reflects changes of residence between 1995 and 2000. Construct a bar graph for these data. Which graph is a more effective display of the data? Explain.

The California Healthy Kids Survey in 1999 and 2001 asked 7th, 9th, and 11th graders in San Luis Obispo County whether they smoked tobacco. In 1999, 6% of 7th graders, 17% of 9th graders, and 23% of 11th graders admitted smoking tobacco while in 2001 the corresponding figures were 3%, 13%, and 22%. Create a comparative bar chart showing bars for 7th graders together, bars for 9th graders together, and bars for 11th graders together. Comment on any interesting features of the chart.

The Institute for Highway Safety tracks which cars are most likely to be stolen by looking at theft claims per 1000 insured vehicles. For cars manufactured between 2001 and 2003, the top five were as follows: Claims per 1000 Type of Vehicle Vehicles 0203 Cadillac Escalade EXT (luxury pickup) 20.2 0203 Nissan Maxima (midsize 4-door car) 17.0 0203 Cadillac Escalade (luxury SUV) 10.2 Dodge Stratus/Chrysler Sebring (midsize 4-door car) 8.3 Dodge Intrepid (large 4-door car) 7.9 Use this information to construct a pie chart.

The article The Need to Be Plugged In (Associated Press, December 22, 2005) described the results of a survey of 1006 adults who were asked about various technologies, including personal computers, cell phones, and DVD players. The accompanying table summarizes the responses to questions about how essential these technologies were. Relative Frequency Personal Cell DVD Response Computer Phone Player Cannot imagine living without .46 .41 .19 Would miss but could do without .28 .25 .35 Could definitely live without .26 .34 .46 Construct a comparative bar chart that shows the distribution of responses for the three different technologies.

Students in California are required to pass an exit exam in order to graduate from high school. The pass rate for San Luis Obispo High School has been rising, as have the rates for San Luis Obispo County and the state of California (San Luis Obispo Tribune, August 17, 2004). The percentage of students that passed the test was as follows: Year District Pass Rate 2002 San Luis Obispo High School 66% 2003 72% 2004 93% 2002 San Luis Obispo County 62% 2003 57% 2004 85% 2002 State of California 32% 2003 43% 2004 74% a. Construct a comparative bar chart that allows the change in the pass rate for each group to be compared. b. Is the change the same for each group? Comment on any difference observed.

A poll conducted by the Associated PressIpsos on public attitudes found that most Americans are convinced that political corruption is a major problem (San Luis Obispo Tribune, December 9, 2005). In the poll, 1002 adults were surveyed. Two of the questions and the summarized responses to these questions follow: How widespread do you think corruption is in public service in America? Hardly anyone 1% A small number 20% A moderate number 39% A lot of people 28% Almost everyone 10% Not sure 2% In general, which elected officials would you say are more ethical? Democrats 36% Republicans 33% Both equally 10% Neither 15% Not sure 6% a. For each question, construct a pie chart summarizing the data. b. For each question construct a segmented bar chart displaying the data. c. Which type of graph (pie chart or segmented bar graph) does a better job of presenting the data? Explain.

Poor fitness in adolescents and adults increases the risk of cardiovascular disease. In a study of 3110 adolescents and 2205 adults (Journal of the American Medical Association, December 21, 2005), researchers found 33.6% of adolescents and 13.9% of adults were unfit; the percentage was similar in adolescent males (32.9%) and females (34.4%), but was higher in adult females (16.2%) than in adult males (11.8%). a. Summarize this information using a comparative bar graph that shows differences between males and females within the two different age groups. b. Comment on the interesting features of your graphical display

A survey of 1001 adults taken by Associated Press Ipsos asked How accurate are the weather forecasts in your area? (San Luis Obispo Tribune, June 15, 2005). The responses are summarized in the table below. Extremely 4% Very 27% Somewhat 53% Not too 11% Not at all 4% Not sure 1% a. Construct a pie chart to summarize this data. b. Construct a bar chart to summarize this data. c. Which of these chartsa pie chart or a bar chart best summarizes the important information? Explain.

The article Online Shopping Grows, But Department, Discount Stores Still Most Popular with Holiday Shoppers (Gallup Poll Analyses, December 2, 2002) included the data in the accompanying table. The data are based on two telephone surveys, one conducted in November 2000 and one in November 2002. Respondents were asked if they were very likely, somewhat likely, not too likely, or not at all likely to do Christmas shopping online.a. Construct a comparative bar chart. What aspects of the chart justify the claim in the title of the article that online shopping grows? b. Respondents were also asked about the likelihood of doing Christmas shopping from mail order catalogues. Use the data in the accompanying table to construct a comparative bar chart. Are the changes in responses from 2000 to 2002 similar to what was observed for online shopping? Explain. Relative Frequency Response 2000 2002 Very likely .12 .13 Somewhat likely .22 .17 Not too likely .20 .16 Not at all likely .46 .54

The article So Close, Yet So Far: Predictors of Attrition in College Seniors (Journal of College Student Development [1998]: 343348) examined the reasons that college seniors leave their college programs before graduating. Forty-two college seniors at a large public university who dropped out before graduation were interviewed and asked the main reason for discontinuing enrollment at the university. Data consistent with that given in the article are summarized in the following frequency distribution: a. Would a bar chart or a pie chart be a better choice for summarizing this data set? Explain. b. Based on your answer to Part (a), construct an appropriate graphical summary of the given data. c. Write a few sentences describing the interesting features of your graphical display.

In a discussion of roadside hazards, the web site highwaysafety.com included a pie chart like the one shown:a. Do you think this is an effective use of a pie chart? Why or why not? b. Construct a bar chart to show the distribution of deaths by object struck. Is this display more effective than the pie chart in summarizing this data set? Explain.

The article Death in Roadwork Zones at Record High (San Luis Obispo Tribune, July 25, 2001) included a bar chart similar to this one:a. Comment on the trend over time in the number of people killed in highway work zones. b. Would a pie chart have also been an effective way to summarize these data? Explain why or why not.

The National Survey on Drug Use and Health, conducted in 2002 and 2003 by the Office of Applied Studies, led to the following state estimates of the total number of people (ages 12 and older) who had smoked within the last month). Number of People State (in thousands) Alabama 976 Alaska 129 Arizona 1215 Arkansas 730 California 5508 Colorado 985 Connecticut 678 Delaware 174 District of Columbia 125 Florida 3355 Georgia 1779 Hawaii 217 Idaho 260 Illinois 2754 Indiana 1427 Iowa 647 Kansas 573 Kentucky 1178 Louisiana 1021 Maine 297 Maryland 1039 Massachusetts 1207 Michigan 2336 Minnesota 1122 Mississippi 680 Missouri 1472 Montana 212 Nebraska 367 Nevada 543 New Hampshire 281 New Jersey 1662 New Mexico 363 New York 4052 North Carolina 2010 North Dakota 145 Ohio 2865 Oklahoma 858a. Construct a stem-and-leaf display using hundreds (of thousands) as the stems and truncating the leaves to the tens (of thousands) digit. b. Write a few sentences describing the shape of the distribution and any unusual observations. c. The three largest values were for California, New York, and Texas. Does this indicate that tobacco use is more of a problem in these states than elsewhere? Explain. d. If you wanted to compare states on the basis of the extent of tobacco use, would you use the data in the given table? If yes, explain why this would be reasonable. If no, what would you use instead as the basis for the comparison?

The Connecticut Agricultural Experiment Station conducted a study of the calorie content of different types of beer. The calorie content (calories per 100 ml) for 26 brands of light beer are (from the web site brewery.org): 29 28 33 31 30 33 30 28 27 41 39 31 29 23 32 31 32 19 40 22 34 31 42 35 29 43 Construct a stem-and-leaf display using stems 1, 2, 3, and 4. Write a sentence or two describing the calorie content of light beers.

The stem-and-leaf display of Exercise 3.16 uses only four stems. Construct a stem-and-leaf display for these data using repeated stems 1H, 2L, 2H, . . . , 4L. For example, the first observation, 29, would have a stem of 2 and a leaf of 9. It would be entered into the display for the stem 2H, because it is a high 2that is, it has a leaf that is on the high end (5, 6, 7, 8, 9).

The article A Nation Ablaze with Change (USA Today, July 3, 2001) gave the accompanying data on percentage increase in population between 1990 and 2000 for the 50 U.S. states. Also provided in the table is a column that indicates for each state whether the state is in the eastern or western part of the United States (the states are listed in order of population size): Percentage State Change East/West California 13.8 W Texas 22.8 W New York 5.5 E Florida 23.5 E Illinois 8.6 E Pennsylvania 3.4 E Ohio 4.7 E Michigan 6.9 E New Jersey 8.9 E Georgia 26.4 E North Carolina 21.4 E Virginia 14.4 E Massachusetts 5.5 E Indiana 9.7 E Washington 21.1 W Tennessee 16.7 E Missouri 9.3 E Wisconsin 9.6 E Maryland 10.8 E Arizona 40.0 W Minnesota 12.4 E Louisiana 5.9 E Alabama 10.1 E Colorado 30.6 W Kentucky 9.7 E South Carolina 15.1 E Oklahoma 9.7 W Oregon 20.4 W Connecticut 3.6 E Iowa 5.4 E Mississippi 10.5 E Kansas 8.5 W

A report from Texas Transportation Institute (Texas A&M University System, 2005) titled Congestion Reduction Strategies included the accompanying data on extra travel time for peak travel time in hours per year per traveler for different sized urban areas. Extra Hours Very Large per Year Urban Areas per Traveler Los Angeles, CA 93 San Francisco, CA 72 Washington DC, VA, MD 69 Very Large per Year Urban Areas per Traveler Atlanta, GA 67 Houston, TX 63 Dallas, Fort Worth, TX 60 Chicago, IL-IN 58 Detroit, MI 57 Miami, FL 51 Boston, MA, NH, RI 51 New York, NY-NJ-CT 49 Phoenix, AZ 49 Philadelphia, PA-NJ-DE-MD 38 Extra Hours per Year Large Urban Areas per Traveler Riverside, CA 55 Orlando, FL 55 San Jose, CA 53 San Diego, CA 52 Denver, CO 51 Baltimore, MD 50 Seattle, WA 46 Tampa, FL 46 Minneapolis, St Paul, MN 43 Sacramento, CA 40 Portland, OR, WA 39 Indianapolis, IN 38 St Louis, MO-IL 35 San Antonio, TX 33 Providence, RI, MA 33 Las Vegas, NV 30 Cincinnati, OH-KY-IN 30 Columbus, OH 29 Virginia Beach, VA 26 Milwaukee, WI 23 New Orleans, LA 18 Kansas City, MO-KS 17 Pittsburgh, PA 14 Buffalo, NY 13 Oklahoma City, OK 12 Cleveland, OH 10 a. Construct a back-to-back stem-and-leaf plot for annual delay per traveler for each of the two different sizes of urban areas. b. Is the following statement consistent with the display constructed in part (a)? Explain. The larger the urban areas, the greater the extra travel time during peak period travel.

The article A Nation Ablaze with Change (USA Today, July 3, 2001) gave the accompanying data on percentage increase in population between 1990 and 2000 for the 50 U.S. states. Also provided in the table is a column that indicates for each state whether the state is in the eastern or western part of the United States (the states are listed in order of population size): Percentage State Change East/West California 13.8 W Texas 22.8 W New York 5.5 E Florida 23.5 E Illinois 8.6 E Pennsylvania 3.4 E Ohio 4.7 E Michigan 6.9 E New Jersey 8.9 E Georgia 26.4 E North Carolina 21.4 E Virginia 14.4 E Massachusetts 5.5 E Indiana 9.7 E Washington 21.1 W Tennessee 16.7 E Missouri 9.3 E Wisconsin 9.6 E Maryland 10.8 E Arizona 40.0 W Minnesota 12.4 E Louisiana 5.9 E Alabama 10.1 E Colorado 30.6 W Kentucky 9.7 E South Carolina 15.1 E Oklahoma 9.7 W Oregon 20.4 W Connecticut 3.6 E Iowa 5.4 E Mississippi 10.5 E Kansas 8.5 W a. Construct a stem-and-leaf display for percentage growth for the data set consisting of all 50 states. Hints: Regard the observations as having two digits to the left of the decimal place. That is, think of an observation such as 8.5 as 08.5. It will also be easier to truncate leaves to a single digit; for example, a leaf of 8.5 could be truncated to 8 for purposes of constructing the display. b. Comment on any interesting features of the data set. Do any of the observations appear to be outliers? c. Now construct a comparative stem-and-leaf display for the eastern and western states. Write a few sentences comparing the percentage growth distributions for eastern and western states.

High school dropout rates (percentages) for the period 19971999 for the 50 states were given in The Chronicle of Higher Education (August 31, 2001) and are shown in the following table: State Rate Alabama 10 Alaska 7 Arizona 17 Arkansas 12 California 9 Colorado 13 State Rate Connecticut 9 Delaware 11 Florida 12 Georgia 13 Hawaii 5 Idaho 10 Illinois 9 Indiana 6 Iowa 7 Kansas 7 Kentucky 11 Louisiana 11 Maine 7 Maryland 7 Massachusetts 6 Michigan 9 Minnesota 6 Mississippi 10 Missouri 9 Montana 8 Nebraska 8 Nevada 17 New Hampshire 7 New Jersey 6 New Mexico 13 New York 9 North Carolina 11 North Dakota 5 Ohio 8 Oklahoma 9 Oregon 13 Pennsylvania 7 Rhode Island 11 South Carolina 9 South Dakota 8 Tennessee 12 Texas 12 Utah 9 Vermont 6 Virginia 8 Washington 8 West Virginia 8 Wisconsin 5 Wyoming 9 Note that dropout rates range from a low of 5% to a high of 17%. In constructing a stem-and-leaf display for these data, if we regard each dropout rate as a two-digit number and use the first digit for the stem, then there are only two possible stems, 0 and 1. One solution is to use repeated stems. Consider a scheme that divides the leaf range into five parts: 0 and 1, 2 and 3, 4 and 5, 6 and 7, and 8 and 9. Then, for example, stem 1 could be repeated as 1. with leaves 0 and 1 1t with leaves 2 and 3 1f with leaves 4 and 5 1s with leaves 6 and 7 If there had been any dropout rates as large as 18 or 19 in the data set, we would also need to include a stem 1* to accommodate the leaves of 8 and 9. Construct a stem-andleaf display for this data set that uses stems 0f, 0s, 0*, 1., 1t, 1f, and 1s. Comment on the important features of the display

Medicares new medical plans offer a wide range of variations and choices for seniors when picking a drug plan (San Luis Obispo Tribune, November 25, 2005). The monthly cost for a stand-alone drug plan varies from plan to plan and from state to state. The accompanying table gives the premium for the plan with the lowest cost for each state. Cost per Month State (dollars) Alabama 14.08 Alaska 20.05 Arizona 6.14 Arkansas 10.31 California 5.41 Colorado 8.62 Connecticut 7.32 Delaware 6.44 District of Columbia 6.44 Florida 10.35 Georgia 17.91 Hawaii 17.18 Idaho 6.33 Illinois 13.32 Indiana 12.30 Iowa 1.87 Kansas 9.48 Kentucky 12.30 Louisiana 17.06 Maine 19.60 Maryland 6.44 Massachusetts 7.32 Michigan 13.75 Minnesota 1.87 Mississippi 11.60 Missouri 10.29 Montana 1.87 Nebraska 1.87 Nevada 6.42 Cost per Month State (dollars) New Hampshire 19.60 New Jersey 4.43 New Mexico 10.65 New York 4.10 North Carolina 13.27 North Dakota 1.87 Ohio 14.43 Oklahoma 10.07 Oregon 6.93 Pennsylvania 10.14 Rhode Island 7.32 South Carolina 16.57 South Dakota 1.87 Tennessee 14.08 Texas 10.31 Utah 6.33 Vermont 7.32 Virginia 8.81 Washington 6.93 West Virginia 10.14 Wisconsin 11.42 Wyoming 1.87 a. Use class intervals of $0 to $3, $3 to $6, $6 to $9 etc., to create a relative frequency distribution for these data. b. Construct a histogram and comment on its shape. c. Using the relative frequency distribution or the histogram, determine the proportion of the states that have a minimum monthly plan of less than $13.00 a month. 3

The following two relative frequency distributions were constructed using data that appeared in the report Undergraduate Students and Credit Cards in 2004 (Nellie Mae, May 2005). One relative frequency distribution is based on credit bureau data for a random sample of 1413 college students, while the other is based on the result of a survey completed by 132 of the 1260 college students who received the survey. Credit Card Balance (dollars) Credit Bureau Data Relative Frequency 0 to 100 .18 100 to 500 .19 500 to 1000 .14 1000 to 2000 .16 2000 to 3000 .10 3000 to 7000 .16 7000 or more .07 Credit Card Balance (dollars) Survey Data Relative Frequency 0 to 100 .18 100 to 500 .22 500 to 1000 .17 1000 to 2000 .22 2000 to 3000 .07 3000 to 7000 .14 7000 or more .00 a. Construct a histogram for the credit bureau data. For purposes of constructing the histogram, assume that none of the students in the sample had a balance higher than 15,000 and that the last interval can be regarded as 7000 to 15,000. Be sure to use the density scale when constructing the histogram. b. Construct a histogram for the survey data. Use the same scale that you used for the histogram in part (a) so that it will be easy to compare the two histograms. c. Comment on the similarities and differences in the histograms from Parts (a) and (b). d. Do you think the high nonresponse rate for the survey may have contributed to the observed differences in the two histograms? Explain. 3.24 Peop

People suffering from Alzheimers disease often have difficulty performing basic activities of daily living (ADLs). In one study (Functional Status and Clinical Findings in Patients with Alzheimers Disease, Journal of Gerontology [1992]: 177182), investigators focused on six such activities: dressing, bathing, transferring, toileting, walking, and eating. Here are data on the number of ADL impairments for each of 240 patients: Number of impairments 0 1 2 3 4 5 6 Frequency 100 43 36 17 24 9 11 a. Determine the relative frequencies that correspond to the given frequencies. b. What proportion of these patients had at most two impairments? c. Use the result of Part (b) to determine what proportion of patients had more than two impairments. d. What proportion of the patients had at least four impairments?

USA Today (July 2, 2001) gave the following information regarding cell phone use for men and women: Average Number of Minutes Used Relative Frequency per Month Men Women 0 to 200 .56 .61 200 to 400 .18 .18 400 to 600 .10 .13 600 to 800 .16 .08 a. Construct a relative frequency histogram for average number of minutes used per month for men. How would you describe the shape of this histogram? b. Construct a relative frequency histogram for average number of minutes used per month for women. Is the distribution for average number of minutes used per month similar for men and women? Explain. c. What proportion of men average less than 400 minutes per month? d. Estimate the proportion of men that average less than 500 minutes per month. e. Estimate the proportion of women that average 450 minutes or more per month. 3.

U.S. Census data for San Luis Obispo County, California, were used to construct the following frequency distribution for commute time (in minutes) of working adults (the given frequencies were read from a graph that appeared in the San Luis Obispo Tribune [September 1, 2002] and so are only approximate):Commute Time Frequency 0 to 5 5,200 5 to 10 18,200 10 to 15 19,600 15 to 20 15,400 20 to 25 13,800 25 to 30 5,700 30 to 35 10,200 35 to 40 2,000 40 to 45 2,000 45 to 60 4,000 60 to 90 2,100 90 to 120 2,200 a. Notice that not all intervals in the frequency distribution are equal in width. Why do you think that unequal width intervals were used? b. Construct a table that adds a relative frequency and a density column to the given frequency distribution. c. Use the densities computed in Part (b) to construct a histogram for this data set. (Note: The newspaper displayed an incorrectly drawn histogram based on frequencies rather than densities!) Write a few sentences commenting on the important features of the histogram. d. Compute the cumulative relative frequencies, and construct a cumulative relative frequency plot. e. Use the cumulative relative frequency plot constructed in Part (d) to answer the following questions. i. Approximately what proportion of commute times were less than 50 min? ii. Approximately what proportion of commute times were greater than 22 min? iii. What is the approximate commute time value that separates the shortest 50% of commute times from the longest 50%? 3.27 The

The article Determination of Most Representative Subdivision (Journal of Energy Engineering [1993]: 43 55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable x
total length of streets within a subdivision are as follows: 1280 5320 4390 2100 1240 3060 4770 1050 360 3330 3380 340 1000 960 1320 530 3350 540 3870 1250 2400 960 1120 2120 450 2250 2320 2400 3150 5700 5220 500 1850 2460 5850 2700 2730 1670 100 5770 3150 1890 510 240 396 1419 2109 5770 a. Construct a stem-and-leaf display for these data using the thousands digit as the stem. Comment on the various features of the display. b. Construct a histogram using class boundaries of 0 to 1000, 1000 to 2000, and so on. How would you describe the shape of the histogram? c. What proportion of subdivisions has total length less than 2000? between 2000 and 4000?

Student loans can add up, especially for those attending professional schools to study in such areas as medicine, law, or dentistry. Researchers at the University of Washington studied medical students and gave the following information on the educational debt of medical students on completion of their residencies (Annals of Internal Medicine [March 2002]: 384398): Educational Relative Debt (dollars) Frequency 0 to 5000 .427 5000 to 20,000 .046 20,000 to 50,000 .109 50,000 to 100,000 .232 100,000 or more .186 a. What are two reasons that it would be inappropriate to construct a histogram using relative frequencies to determine the height of the bars in the histogram? b. Suppose that no student had an educational debt of $150,000 or more upon completion of his or her residency, so that the last class in the relative frequency distribution would be 100,000 to 150,000. Summarize this distribution graphically by constructing a histogram of the educational debt data. (Dont forget to use the density scale for the heights of the bars in the histogram, because the interval widths arent all the same.) c. Based on the histogram of Part (b), write a few sentences describing the educational debt of medical students completing their residencies. 3.3

An exam is given to students in an introductory statistics course. What is likely to be true of the shape of the histogram of scores if: a. the exam is quite easy? b. the exam is quite difficult? c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes mathematical manipulation? Explain your reasoning in each case.

The paper Lessons from Pacemaker Implantations (Journal of the American Medical Association [1965]: 231232) gave the results of a study that followed 89 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of the pacemaker was recorded: 24 20 16 32 14 22 2 12 24 6 10 20 8 16 12 24 14 20 18 14 16 18 20 22 24 26 28 18 14 10 12 24 6 12 18 16 34 18 20 22 24 26 18 2 18 12 12 8 24 10 14 16 22 24 22 20 24 28 20 22 26 20 6 14 16 18 24 18 16 6 16 10 14 18 24 22 28 24 30 34 26 24 22 28 30 22 24 22 32 30 34 26 24 22 28 a. Summarize these data in the form of a frequency distribution, using class intervals of 0 to 6, 6 to 12, and so on. b. Compute the relative frequencies and cumulative relative frequencies for each class interval of the frequency distribution of Part (a). c. Show how the relative frequency for the class interval 12 to 18 could be obtained from the cumulative relative frequencies. d. Use the cumulative relative frequencies to give approximate answers to the following: i. What proportion of those who participated in the study had pacemakers that did not malfunction within the first year? ii. If the pacemaker must be replaced as soon as the first electrical malfunction occurs, approximately what proportion required replacement between 1 and 2 years after implantation? e. Construct a cumulative relative frequency plot, and use it to answer the following questions. i. What is the approximate time at which about 50% of the pacemakers had failed? ii. What is the approximate time at which only about 10% of the pacemakers initially implanted were still functioning? 3

The clearness index was determined for the skies over Baghdad for each of the 365 days during a particular year (Contribution to the Study of the Solar Radiation Climate of the Baghdad Environment, Solar Energy [1990]: 712). The accompanying table summarizes the resulting data: Number of Days Clearness Index (frequency) 0.15 to 0.25 8 0.25 to 0.35 14 0.35 to 0.45 28 0.45 to 0.50 24 0.50 to 0.55 39 0.55 to 0.60 51 0.60 to 0.65 106 0.65 to 0.70 84 0.70 to 0.75 11 a. Determine the relative frequencies and draw the corresponding histogram. (Be careful herethe intervals do not all have the same width.) b. Cloudy days are those with a clearness index smaller than 0.35. What proportion of the days was cloudy? c. Clear days are those for which the index is at least 0.65. What proportion of the days was clear? 3.32 Ho

How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35 km and 40 km points, and then subtracting the 5-km time from the 3540-km time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The histogram on page 117 is based on times of runners who participated in several different Japanese marathons (Factors Affecting Runners Marathon Performance, Chance [Fall, 1993]: 2430). What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?

Construct a histogram corresponding to each of the five frequency distributions, IV, given in the following table, and state whether each histogram is symmetric, bimodal, positively skewed, or negatively skewed: Frequency Class Interval I II III IV V 0 to 10 5 40 30 15 6 10 to 20 10 25 10 25 5 20 to 30 20 10 8 8 6 30 to 40 30 8 7 7 9 40 to 50 20 7 7 20 9 50 to 60 10 5 8 25 23 60 to 70 5 5 30 10 42 3.34

Using the five class intervals 100 to 120, 120 to 140, . . . , 180 to 200, devise a frequency distribution based on 70 observations whose histogram could be described as follows: a. symmetric c. positively skewed b. bimodal d. negatively skewed

Does the size of a transplanted organ matter? A study that attempted to answer this question (Minimum Graft Size for Successful Living Donor Liver Transplantation, Transplantation [1999]:11121116) presented a scatterplot much like the following (graft weight ratio is the weight of the transplanted liver relative to the ideal size liver for the recipient): a. Discuss interesting features of this scatterplot. b. Why do you think the overall relationship is negative?

Data on x
poverty rate (%) and y
high school dropout rate (%) for the 50 U.S. states and the District of Columbia were used to construct the following scatterplot (Chronicle of Higher Education, August 31, 2001)Write a few sentences commenting on this scatterplot. Would you describe the relationship between poverty rate and dropout rate as positive (y tends to increase as x increases), negative (y tends to decrease as x increases), or as having no discernible relationship between x and y?

A number of studies concerning muscular effi- ciency in humans have used competitive cyclists as subjects. It had previously been observed that variation in efficiency could not be explained by differences in cycling technique. The paper Cycling Efficiency Is Related to the Percentage of Type I Muscle Fibers (Medicine and Science in Sports and Exercise [1992]: 782788) reported the accompanying data on x
percentage of type I (slow twitch) muscle fibers and y
cycling gross efficiency (the ratio of work accomplished per minute to caloric expenditure)

The article Exhaust Emissions from Four-Stroke Lawn Mower Engines (Journal of the Air and Water Management Association [1997]: 945952) reported data from a study in which both a baseline gasoline and a reformulated gasoline were used. Consider the following observations on age (in years) and NOx emissions (in grams per kilowatt-hour): Engine Age Baseline Reformulated 1 0 1.72 1.88 2 0 4.38 5.93 3 2 4.06 5.54 4 11 1.26 2.67 5 7 5.31 6.53 6 16 0.57 0.74 7 9 3.37 4.94 8 0 3.44 4.89 9 12 0.74 0.69 10 4 1.24 1.42 a. Construct a scatterplot of emissions versus age for the baseline gasoline. b. Construct a scatterplot of emissions versus age for the reformulated gasoline. c. Do age and emissions appear to be related? If so, in what way? d. Comment on the similarities and differences in the two scatterplots of Parts (a) and (b).

One factor in the development of tennis elbow, a malady that strikes fear into the hearts of all serious players of that sport (including one of the authors), is the impact-induced vibration of the racket-and-arm system at ball contact. It is well known that the likelihood of getting tennis elbow depends on various properties of the racket used. Consider the accompanying scatterplot of x
racket resonance frequency (in hertz) and y
sum of peak-topeak accelerations (a characteristic of arm vibration, in meters per second per second) for n
23 different rackets (Transfer of Tennis Racket Vibrations into the Human Forearm, Medicine and Science in Sports and Exercise [1992]: 11341140). Discuss interesting features of the data and of the scatterplot.

Stress can affect the physiology and behavior of animals, just as it can with humans (as many of us know all too well). The accompanying data on x
plasma cortisol concentration (in milligrams of cortisol per milliliter of plasma) and y
oxygen consumption rate (in milligrams per kilogram per hour) for juvenile steelhead after three 2-min disturbances were read from a graph in the paper Metabolic Cost of Acute Physical Stress in Juvenile Steelhead (Transactions of the American Fisheries Society [1987]: 257263). The paper also included data for unstressed fish. x 25 36 48 59 62 72 80 100 100 137 y 155 184 180 220 280 163 230 222 241 350 a. Is the value of y determined solely by the value of x? Explain your reasoning. b. Construct a scatterplot of the data. c. Does an increase in plasma cortisol concentration appear to be accompanied by a change in oxygen consumption rate? Comment.

The National Telecommunications and Information Administration published a report titled Falling Through the Net: Toward Digital Inclusion (U.S. Department of Commerce, October 2000) that included the following information on access to computers in the home: Percentage of Households Year with a Computer 1985 8.2 1990 15.0 1994 22.8 1995 24.1 1998 36.6 1999 42.1 2000 51.0 a. Construct a time-series plot for these data. Be careful the observations are not equally spaced in time. The points in the plot should not be equally spaced along the x axis. b. Comment on any trend over time.

According to the National Association of Home Builders, the average size of a home in 1950 was 983 ft2 . The average size increased to 1500 ft2 in 1970, 2080 ft2 in 1990; and 2330 ft2 in 2003 (San Luis Obispo Tribune, October 16, 2005). a. Construct a time-series plot that shows how the average size of a home has changed over time. b. If the trend of the time-series plot were to continue, what would you predict the average home size to be in 2010?

An article that appeared in USA Today (September 3, 2003) included a graph similar to the one show here summarizing responses from polls conducted in 1978, 1991, and 2003 in which a sample of American adults were asked whether or not it was a good time or a bad time to buy a house. a. Construct a time-series plot that shows how the percentage that thought it was a good time to buy a house has changed over time. b. Add a new line to the plot from Part (a) showing the percentage that thought it was a bad time to buy a house over time. Be sure to label the lines clearly. c. Which graph, the given bar chart or the time-series plot, best shows the trend over time?

Some days of the week are more dangerous than others, according to Traffic Safety Facts produced by the National Highway Traffic Safety Administration. Average number of fatalities per day for each day of the week are shown in the accompanying table. Good time Bad time 53% 67% 78% 78% 29% 25% 19% 20% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% Mar-78 Mar-91 Jun-03 Sep-03 126 Chapter 3 Graphical Methods for Describing Data Bold exercises answered in back Data set available online but not required Video solution available Average Fatalities per Day (day of the week) Mon Tue Wed Thurs Fri Sat Sun 19781982 103 101 107 116 156 201 159 19831987 98 96 99 108 140 174 140 19881992 97 94 97 106 139 168 135 19931997 97 93 96 102 129 148 127 19982002 99 96 98 104 129 149 130 Total 99 96 100 107 138 168 138 a. Using the midpoint of each year range (e.g., 1980 for the 19781982 range), construct a time-series plot that shows the average fatalities over time for each day of the week. Be sure to label each line clearly as to which day of the week it represents. b. Write a sentence or two commenting on the difference in average number of fatalities for the days of the week. What is one possible reason for the differences? c. Write a sentence or two commenting on the change in average number of fatalities over time. What is one possible reason for the change?

The accompanying time-series plot of movie box office totals (in millions of dollars) over 18 weeks of summer for both 2001 and 2002 appeared in USA Today (September 3, 2002): Patterns that tend to repeat on a regular basis over time are called seasonal patterns. Describe any seasonal patterns that you see in the summer box office data. Hint: Look for patterns that seem to be consistent from year to year.

Working as a class, decide how you will select a sample that you think will be representative of the students from your school

Use the sampling method from Step 1 to obtain the subjects for this study. Subjects should be shown the accompanying map of the United States and asked to point out the state of Vermont. After the subject has given his or her answer, ask the subject to point out the state of Nebraska. For each subject, record whether or not Vermont was correctly identified and whether or not Nebraska was correctly identified.

When the data collection process is complete, summarize the resulting data in a table like the one shown here: Response Frequency Correctly identified both states Correctly identified Vermont but not Nebraska Correctly identified Nebraska but not Vermont Did not correctly identify either state

Construct a pie chart that summarizes the data in the table from Step 3.

What proportion of sampled students were able to correctly identify Vermont on the map?

What proportion of sampled students were able to correctly identify Nebraska on the map?

Construct a comparative bar chart that shows the proportion correct and the proportion incorrect for each of the two states considered.

Which state, Vermont or Nebraska, is closer to the state in which your school is located? Based on the pie chart, do you think that the students at your school were better able to identify the state that was closer than the one that was farther away? Justify your answer.

Write a paragraph commenting on the level of knowledge of U.S. geography demonstrated by the students participating in this study.

Would you be comfortable generalizing your conclusions in Step 8 to the population of students at your school? Explain why or why not.

Flip a coin to determine which hand you will measure first. If the coin lands heads side up, start with the right hand. If the coin lands tails side up, start with the left hand. With the designated hand, reach into the bowl and grab as many beans as possible. Raise the hand over the bowl and count to 4. If no beans drop during the count to 4, drop the beans onto a piece of paper and record the number of beans grabbed. If any beans drop during the count, restart the count. That is, you must hold the beans for a count of 4 without any beans falling before you can determine the number grabbed. Repeat the process with the other hand, and then record the following information: (1) right-hand number, (2) left-hand number, and (3) dominant hand (left or right, depending on whether you are left- or righthanded).

Create a class data set by recording the values of the three variables listed in Step 1 for each student in your class.

Using the class data set, construct a comparative stemand-leaf display with the right-hand counts displayed on the right and the left-hand counts displayed on the left of the stem-and-leaf display. Comment on the interesting features of the display and include a comparison of the righthand count and left-hand count distributions.

Now construct a comparative stem-and-leaf display that allows you to compare dominant-hand count to nondominant-hand count. Does the display support the theory that dominant-hand count tends to be higher than nondominant-hand count?

For each observation in the data set, compute the difference dominant-hand count  nondominant-hand count Construct a stem-and-leaf display of the differences. Comment on the interesting features of this display.

Explain why looking at the distribution of the differences (Step 5) provides more information than the comparative stem-and-leaf display (Step 4). What information is lost in the comparative display that is retained in the display of the differences?

Each year the College Board publishes a profile of students taking the SAT. In the report 2005 College Bound Seniors: Total Group Profile Report, the average SAT scores were reported for three groups defined by first language learned. Use the data in the accompanying table to construct a bar chart of the average verbal SAT score for the three groups. First Language Learned Average Verbal SAT English 519 English and another language 486 A language other than English 462

The report referenced in Exercise 3.46 also gave average math SAT scores for the three language groups, as shown in the following table. First Language Learned Average Math SAT English 521 English and another language 513 A language other than English 521 Construct a comparative bar chart for the average verbal and math scores for the three language groups. Write a few sentences describing the differences and similarities between the three language groups as shown in the bar chart

Each student in a sample of 227 boys and 251 girls was asked what he or she thought was most important: getting good grades, being popular, or being good at sports. The resulting data, from the paper The Role of Sport as a Social Determinant for Children (Research Quarterly for Exercise and Sport [1992]: 418424), are summarized in the accompanying table: Construct a comparative bar chart for this data set. Remember to use relative frequency when constructing the bar chart because the two group sizes are not the same.

The paper Community Colleges Start to Ask, Where Are the Men? (Chronicle of Higher Education, June 28, 2002) gave data on gender for community college students. It was reported that 42% of students enrolled at community colleges nationwide were male and 58% were female. Construct a segmented bar graph for these data.

The article Tobacco and Alcohol Use in G-Rated Childrens Animated Films (Journal of the American Medical Association [1999]: 11311136) reported exposure to tobacco and alcohol use in all G-rated animated films released between 1937 and 1997 by five major film studios. The researchers found that tobacco use was shown in 56% of the reviewed films. Data on the total tobacco exposure time (in seconds) for films with tobacco use produced by Walt Disney, Inc., were as follows: 223 176 548 37 158 51 299 37 11 165 74 92 6 23 206 9 299 37 11 165 Data for 11 G-rated animated films showing tobacco use that were produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox were also given. The tobacco exposure times (in seconds) for these films was as follows: 205 162 6 1 117 5 91 155 24 55 17 Construct a comparative stem-and-leaf display for these data. Comment on the interesting features of this display.

The accompanying data on household expenditures on transportation for the United Kingdom appeared in Transport Statistics for Great Britain: 2002 Edition (in Family Spending: A Report on the Family Expenditure Survey [The Stationary Office, 2002]). Expenditures (in pounds per week) included costs of purchasing and maintaining any vehicles owned by members of the household and any costs associated with public transportation and leisure travel. Percentage Average of Household Transportation Expenditures Year Expenditure for Transportation 1990 247.20 16.2 1991 259.00 15.3 1992 271.80 15.8 1993 276.70 15.6 1994 283.60 15.1 1995 289.90 14.9 1996 309.10 15.7 1997 328.80 16.7 1998 352.20 17.0 1999 359.40 17.2 2000 385.70 16.7 a. Construct time-series plots of the transportation expense data and the percent of household expense data. b. Do the time-series plots of Part (a) support the statement that follows? Explain why or why not. Statement: Although actual expenditures have been increasing, the percentage of the total household expenditures that was for transportation has remained relatively stable.

The web site PollingReport.com gave data from a CBS news poll conducted in December 1999. In the survey described, people were asked the following question: All things considered, in our society today, do you think there are more advantages in being a man, more advantages in being a woman, or are there no more advantages in being one than the other? Responses for men and for women are summarized in the following table: Relative Frequency Response Women Men Advantage in being a man .57 .41 Advantage in being a woman .06 .14 No advantage .33 .40 Dont know .04 .05 Construct a comparative bar chart for the response, and write a few sentences describing the differences in the response distribution for men and women.

The same poll described in Exercise 3.52 also asked the question, What about salaries? These days, if a man and a woman are doing the same work, do you think the man generally earns more, the woman generally earns more, or that both earn the same amount? The resulting data are shown in the following table: Relative Frequency Response Women Men Man earns more .70 .59 Woman earns more .01 .01 Both earn the same .25 .34 Dont know .04 .06 a. Construct a comparative bar chart that allows the responses for women and men to be compared.b. Construct two pie charts, one summarizing the responses for women and one summarizing the responses for men. c. Is it easier to compare the responses of women and men by looking at the comparative bar chart or the two pie charts? Explain. d. Write a brief paragraph describing the difference between women and men with respect to the way they answered this question.

The article The Healthy Kids Survey: A Look at the Findings (San Luis Obispo Tribune, October 25, 2002) gave the accompanying information for a sample of fifth graders in San Luis Obispo County. Responses are to the question: After school, are you home alone without adult supervision? Response Percentage Never 8 Some of the time 15 Most of the time 16 All of the time 61 a. Summarize these data using a pie chart. b. Construct a segmented bar chart for these data. c. Which graphing methodthe pie chart or the segmented bar chartdo you think does a better job of conveying information about response? Explain.

If you were taking a new job and had your choice of a boss, would you prefer to work for a man or a woman? That was the question posed to individuals in a sample of 576 employed adults (Gallup at a Glance, October 16, 2002). Responses are summarized in the following table: Response Frequency Prefer to work for a man 190 Prefer to work for a woman 92 No difference 282 No opinion 12 a. Construct a pie chart to summarize this data set, and write a sentence or two summarizing how people responded to this question. b. Summarize the given data using a segmented bar chart.

The accompanying stem-and-leaf display shows observations on average shower flow rate (in liters per minute) for a sample of 129 houses in Perth, Australia (An Application of Bayes Methodology to the Analysis of Diary Records from a Water Use Study, Journal of the American Statistical Association [1987]: 705711). 2 23 3 2344567789 4 01356889 5 00001114455666789 6 0000122223344456667789999 7 00012233455555668 8 02233448 9 012233335666788 10 2344455688 11 2335999 12 37 13 8 Stem: Ones 14 36 Leaf: Tenths 15 0035 16 17 18 9 a. What is the smallest flow rate in the sample? b. If one additional house yielded a flow rate of 8.9, where would this observation be placed on the display? c. What is a typical, or representative, flow rate? d. Does the display appear to be highly concentrated, or quite spread out? e. Does the distribution of values in the display appear to be reasonably symmetric? If not, how would you describe the departure from symmetry? f. Does the data set appear to contain any outliers (observations far removed from the bulk of the data)?

Disparities among welfare payments by different states have been the source of much political controversy. The accompanying table reports average payment per person (in dollars) in the Aid to Families with Dependent Children Program for the 1990 fiscal year. Construct a relative frequency distribution for these data using equal interval widths. Draw the histogram corresponding to your frequency distribution. State Average Welfare Payment ($) Alaska 244.90 California 218.31 Arizona 93.57 Montana 114.95

2005 was a record year for hurricane devastation in the United States (San Luis Obispo Tribune, November 30, 2005). Of the 26 tropical storms and hurricanes in the season, 4 hurricanes hit the mainland: Dennis, Katrina, Rita, and Wilma. The U.S. insured catastrophic losses since 1989 (approximate values read from a graph that appeared in the San Luis Obispo Tribune, November 30, 2005) are as follows: Year Cost (in billions of dollars) 1989 7.5 1990 2.5 1991 4.0 1992 22.5 1993 5.0 1994 18.0 1995 9.0 1996 8.0 1997 2.6 1998 10.0 1999 9.0 2000 3.0 2001 27.0 2002 5.0 2003 12.0 2004 28.5 2005 56.8 Construct a time-series plot that shows the insured catastrophic loss over time. What do you think causes the peaks in the graph?

Each observation in the following data set is the number of housing units (homes or condominiums) sold during November 1992 in a region corresponding to a particular Orange County, California, ZIP code: 25 18 16 6 26 11 29 7 5 15 12 37 35 11 16 35 20 27 17 30 10 16 28 13 26 11 12 8 9 29 0 20 30 12 45 26 21 30 18 31 0 46 47 14 13 29 11 18 10 27 5 18 67 21 35 48 42 70 43 0 30 17 35 40 61 18 17 17 13 29 11 18 Construct a stem-and-leaf display, and comment on any interesting features

Each murder committed in Utah during the period 19781990 was categorized by day of the week, resulting in the following frequencies: Sunday, 109; Monday, 73; Tuesday, 97; Wednesday, 95; Thursday, 83; Friday, 107; Saturday, 100. a. Construct the corresponding frequency distribution. b. What proportion of these murders was committed on a weekend daythat is, Friday, Saturday, or Sunday? c. Do these data suggest that a murder is more likely to be committed on some days than on other days? Explain your reasoning

An article in the San Luis Obispo Tribune (November 20, 2002) stated that 39% of those with critical housing needs (those who pay more than half their income for housing) lived in urban areas, 42% lived in suburban areas, and the rest lived in rural areas. Construct a pie chart that shows the distribution of type of residential area (urban, suburban, or rural) for those with critical housing needs.

Living-donor kidney transplants are becoming more common. Often a living donor has chosen to donate a kidney to a relative with kidney disease. The following data appeared in a USA Today article on organ transplants (Kindness Motivates Newest Kidney Donors, June 19, 2002): Number of Kidney Transplants Living-Donor Living-Donor to Year to Relative Unrelated Person 1994 2390 202 1995 2906 400 1996 2916 526 1997 3144 607 1998 3324 814 1999 3359 930 2000 3679 1325 2001 3879 1399 a. Construct a time-series plot for the number of livingdonor kidney transplants where the donor is a relative of the recipient. Describe the trend in this plot. b. Use the data from 1994 and 2001 to construct a comparative bar chart for the type of donation (relative or unrelated). Write a few sentences commenting on your display

Many nutritional experts have expressed concern about the high levels of sodium in prepared foods. The following data on sodium content (in milligrams) per frozen meal appeared in the article Comparison of Light Frozen Meals (Boston Globe, April 24, 1991): 720 530 800 690 880 1050 340 810 760 300 400 680 780 390 950 520 500 630 480 940 450 990 910 420 850 390 600 Two histograms for these data are shown: a. Do the two histograms give different impressions about the distribution of values? b. Use each histogram to determine approximately the proportion of observations that are less than 800, and compare to the actual proportion.

Americium 241 ( 241Am) is a radioactive material used in the manufacture of smoke detectors. The article Retention and Dosimetry of Injected 241Am in Beagles (Radiation Research [1984]: 564575) described a study in which 55 beagles were injected with a dose of 241Am (proportional to each animals weight). Skeletal retention of 241Am (in microcuries per kilogram) was recorded for each beagle, resulting in the following data: 0.196 0.451 0.498 0.411 0.324 0.190 0.489 0.300 0.346 0.448 0.188 0.399 0.305 0.304 0.287 0.243 0.334 0.299 0.292 0.419 0.236 0.315 0.447 0.585 0.291 0.186 0.393 0.419 0.335 0.332 0.292 0.375 0.349 0.324 0.301 0.333 0.408 0.399 0.303 0.318 0.468 0.441 0.306 0.367 0.345 0.428 0.345 0.412 0.337 0.353 0.357 0.320 0.354 0.361 0.329 0.337 a. Construct a frequency distribution for these data, and draw the corresponding histogram. b. Write a short description of the important features of the shape of the histogram.