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: 59, 53, 69, 87, 71, 65, 98, 88, 85, 92, 90, 91, 65, 67, 88, 87, 72, 60, 71, 76, 73, 74, 86, 83, 89, 56, 78, 77, 83, 92, 57, 46 (a) make a stem-and-leaf display for these data. (enter numbers from smallest to largest separated by spaces. enter none for stems with no values.) stem | leaf 4 | 5 | 6 | 7 | 8 | 9 | (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? sort of, these cowboys lived somewhat long lives, as evidenced by the high frequency of leaves for stems 5 and 6 (i.e., 50-year-old and 60-year-old). no, these cowboys did not live long lives, as evidenced by the high frequency of leaves for stems 4 and 5 (i.e., 40-year-old and 50-year-old). yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-year-old, 80-year-old, and 90-year-old).

Explanation:

Part (a)

Step 1: Identify stems and leaves

Stems are the tens digits, leaves are the units digits. We list each data point's tens (stem) and units (leaf) part.
Data: 46, 53, 56, 57, 59, 60, 65, 65, 67, 69, 71, 71, 73, 74, 76, 77, 78, 83, 85, 86, 87, 87, 88, 88, 89, 90, 91, 92, 92, 98 (wait, original data has 32 points, let's re - list all:
First row: 59, 53, 69, 87, 71, 65, 98, 88, 85, 92, 90, 91, 65, 67, 88, 87
Second row: 72, 60, 71, 76, 73, 74, 86, 83, 89, 56, 78, 77, 83, 92, 57, 46

Now, group by stem (tens place):

• Stem 4: Only 46, so leaf is 6.
• Stem 5: Numbers are 53, 56, 57, 59. Leaves: 3, 6, 7, 9 (sorted).
• Stem 6: Numbers are 60, 65, 65, 67, 69. Leaves: 0, 5, 5, 7, 9 (sorted).
• Stem 7: Numbers are 71, 71, 72, 73, 74, 76, 77, 78. Leaves: 1, 1, 2, 3, 4, 6, 7, 8 (sorted).
• Stem 8: Numbers are 83, 83, 85, 86, 87, 87, 88, 88, 89. Leaves: 3, 3, 5, 6, 7, 7, 8, 8, 9 (sorted).
• Stem 9: Numbers are 90, 91, 92, 92, 98. Leaves: 0, 1, 2, 2, 8 (sorted).

Step 2: Construct stem - and - leaf display

Stem	Leaf
5	3 6 7 9
6	0 5 5 7 9
7	1 1 2 3 4 6 7 8
8	3 3 5 6 7 7 8 8 9
9	0 1 2 2 8

Part (b)

We analyze the stem - and - leaf display. Stems 7, 8, 9 correspond to ages 70+, 80+, 90+. The high frequency of leaves in these stems shows that many cowboys lived to be 70, 80, or 90 years old, indicating long lives, which supports the quote.

Answer:

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