Real Cowboys' Lifespan: Debunking Wild West Myths

Cowboys: Longevity How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: 58 52 68 86 72 66 97 89 84 91 91 92 66 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 (a) Make a stem-and-leaf display for these data. (b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols. Does the data distribution of longevity lend credence to this quote?

Ecology: Habitat Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is as follows: 46 37 36 42 81 20 73 59 35 50 87 52 24 27 38 56 39 74 56 31 27 91 46 9 54 52 30 33 28 35 35 23 90 72 85 42 59 50 49 48 38 60 46 87 50 89 49 67 Make a stem-and-leaf display of these data. Be sure to indicate the scale. How are the percentages distributed? Is the distribution skewed? Are there any gaps?

Health Care: Hospitals The American Medical Association Center for Health Policy Research included data, by state, on the number of community hospitals and the average patient stay (in days) in its publication State Health Care Data: Utilization, Spending, and Characteristics. The data (by state) are shown in the table. Make a stem-and-leaf display of the data for the average length of stay in days. Comment about the general shape of the distribution.

Health Care: Hospitals Using the number of hospitals per state listed in the table in Problem 3, make a stem-and-leaf display for the number of community hospitals per state. Which states have an unusually high number of hospitals?

Expand Your Knowledge: Split Stem The Boston Marathon is the oldest and best known U.S. marathon. It covers a route from Hopkinton, Massachusetts, to downtown Boston. The distance is approximately 26 miles. Visit the Brase/Brase statistics site at college.hmco.com/pic/braseUS9e and find the link to the Boston Marathon. Search the marathon site to find a wealth of information about the history of the race. In particular, the site gives the winning times for the Boston Marathon. They are all over 2 hours. The following data are the minutes over 2 hours for the winning male runners: 19611980 23 23 18 19 16 17 15 22 13 10 18 15 16 13 9 20 14 10 9 12 19812000 9 8 9 10 14 7 11 8 9 8 11 8 9 7 9 9 10 7 9 9 (a) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the years 1961 to 1980. Use two lines per stem.

Split Stem: Golf The U.S. Open Golf Tournament was played at Congressional Country Club, Bethesda, Maryland, with prizes ranging from $465,000 for first place to $5000. Par for the course is 70. The tournament consists of four rounds played on different days. The scores for each round of the 32 players who placed in the money (more than $17,000) were given on a web site. For more information, visit the Brase/Brase statistics site at college.hmco.com/pic/braseUS9e and find the link to golf. The scores for the first round were as follows: 71 65 67 73 74 73 71 71 74 73 71 70 75 71 72 71 75 75 71 71 74 75 66 75 75 75 71 72 72 73 71 67 The scores for the fourth round for these players were as follows: 69 69 73 74 72 72 70 71 71 70 72 73 73 72 71 71 71 69 70 71 72 73 74 72 71 68 69 70 69 71 73 74 (a) Make a stem-and-leaf display for the first-round scores. Use two lines per stem. (See Problem 5.) (b) Make a stem-and-leaf display for the fourth-round scores. Use two lines per stem. (c) Compare the two distributions. How do the highest scores compare? How do the lowest scores compare? Are cigarettes bad for people? Cigarette smoking involves tar, carbon monoxide, and nicotine. The first two are definitely not good for a persons health, and the last ingredient can cause addiction. Problems 7, 8, and 9 refer to Table 2-16, which was taken from the web site maintained by the Journal of Statistics Education. For more information, visit the Brase/Brase statistics site at college.hmco.com/pic/braseUS9e and find the link to the Journal of Statistics Education. Follow the links to the cigarette data.

Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of tar per cigarette smoked. Are there any outliers?

Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of carbon monoxide per cigarette smoked. Are there any outliers?

Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem (see Problem 5, part a).

Expand Your Knowledge: Back-to-Back Stem Plot In archaeology, the depth (below surface grade) at which artifacts are found is very important. Greater depths sometimes indicate older artifacts, perhaps from a different archaeological period. Figure 2-17 is a back-to-back stem plot showing the depths of artifact locations at two different archaeological sites. These sites are from similar geographic locations. Notice that the stems are in the center of the diagram. The leaves for Site I artifact depths are shown to the left of the stem, while the leaves for Site II are to the right of the stem (see Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre, University of New Mexico Press). (a) What are the least and greatest depths of artifact finds at Site I? at Site II? (b) Describe the data distribution of depths of artifact finds at Site I and at Site II. (c) At Site II, there is a gap in the depths at which artifacts were found. Does the Site II data distribution suggest that there might have been a period of no occupation?