Question

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. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Longevity of Cowboys 4 5 6 7 8 9 7 2788 16688 02233567 44456679 011237 (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? No, these cowboys did not live long lives, as evidenced by the high frequency of leaves for stems 4 and 5 (i.e., 40- and 50-year-olds). Sort of, these cowboys lived somewhat long lives, as evidenced by the high frequency of leaves for stems 5 and 6 (i.e., 50- and 60-year-olds). Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds). 6.–/2.85 points BBUnderStat12 2.1.017. Ask Your Teacher My Notes Question Part Points 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). 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 For this problem, use five classes. (a) Find the class width. 12 (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.) Class Limits Class Boundaries Midpoint Frequency Relative Frequency Cumulative Frequency 1 − 12 13 − 24 25 − 36 37 − 48 49 − 60 0.5 − 12.5 12.5 − 24.5 24.5 − 36.5 36.5 − 48.5 48.5 − 60.5 6.5 18.5 30.5 42.5 54.5 6 10 5 13 8 0.14 0.24 0.12 0.31 0.19 6 10 21 34 42 (c) Draw a histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Draw a relative-frequency histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (e) Categorize the basic distribution shape. uniform mound-shaped symmetrical bimodal skewed left skewed right

Answer 1

a) Stem-and-leaf plot:

Longevity of Cowboys
4	7
5	2 7 8 8
6	1 6 6 8 8
7	0 2 2 3 3 5 6 7
8	4 4 4 5 6 6 7 9
9	0 1 1 2 3 7

b) Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds)

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a) Class width = 12

b)

Class interval	Class Boundaries	Frequency	Relative frequency	Cumulative Frequency
1 - 12	0.5 - 12.5	6	6 / 42 = 0.14	6
13 - 24	12.5 - 24.5	10	10 / 42 = 0.24	16
25 - 36	24.5 - 36.5	5	5 / 42 = 0.12	21
37 - 48	36.5 - 48.5	13	13 / 42 = 0.31	34
49 - 60	48.5 - 60.5	8	8 / 42 = 0.19	42

c) Histogram:

d) Relative Frequency Histogram:

e) Shape : bimodal