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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: $$ \begin{array}{lllllllllll} 58 & 52 & 68 & 86 & 72 & 66 & 97 & 89 & 84 & 91 & 91 \\ 92 & 66 & 68 & 87 & 86 & 73 & 61 & 70 & 75 & 72 & 73 \\ 85 & 84 & 90 & 57 & 77 & 76 & 84 & 93 & 58 & 47 & \end{array} $$ (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?

A data set has values ranging from a low of 10 to a high of 50. The class width is to be 10 . What's wrong with using the class limits \(10-20\), 21-31, 32-42, 43-53 for a frequency table with a class width of 10 ?

The following data represent salaries, in thousands of dollars, for employees of a small company. Notice the data have been sorted in increasing order. $$ \begin{array}{lllllllllllll} 24 & 25 & 25 & 27 & 27 & 29 & 30 & 35 & 35 & 35 & 36 & 38 & 38 \\ 39 & 39 & 40 & 40 & 40 & 45 & 45 & 45 & 45 & 47 & 52 & 52 & 52 \\ 58 & 59 & 59 & 61 & 61 & 67 & 68 & 68 & 68 & 250 & & & \end{array} $$ (a) Make a histogram using the class boundaries \(23.5,69.5,115.5,161.5\), \(207.5,253.5\). (b) Look at the last data value. Does it appear to be an outlier? Could this be the owner's salary? (c) Eliminate the high salary of 250 thousand dollars. Make a new histogram using the class boundaries \(23.5,32.5,41.5,50.5,59.5,68.5 .\) Does this histogram reflect the salary distribution of most of the employees better than the histogram in part (a)?

Use the specified number of classes to do the following. (a) Find the class width. (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (c) Draw a histogram. (d) Draw a relative-frequency histogram. (e) Categorize the basic distribution shape as uniform, mound-shaped symmetrical, bimodal, skewed left, or skewed right. (f) Draw an ogive. Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D. P. Byar, Journal of Urology, Vol. 10, pp. \(556-561)\). Note: These data are also available for download on-line in HM StatSPACE \(^{TM}\). $$ \begin{array}{lrrrrrrrrr} 19 & 18 & 17 & 1 & 21 & 22 & 54 & 46 & 25 & 49 \\ 50 & 1 & 59 & 39 & 43 & 39 & 5 & 9 & 38 & 18 \\ 14 & 45 & 54 & 59 & 46 & 50 & 29 & 12 & 19 & 36 \\ 38 & 40 & 43 & 41 & 10 & 50 & 41 & 25 & 19 & 39 \\ 27 & 20 & & & & & & & & \\ & & & & & \end{array} $$ Use five classes.