Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages.
65, 42, 41, 43, 37, 56, 45, 48, 47, 20, 52, 68, 53, 43, 67,
69, 52, 47, 54, 24, 37, 64, 42, 44, 32, 35, 42, 38, 20, 44,
65, 33, 38, 42, 29, 34, 49, 36, 32, 55.
construct a stem - and - leaf plot for the data. complete parts a. and b.
a. determine the leaves for each corresponding stem. complete the table below.
(use ascending order.)
stem
leaves
2

Explanation:

Step1: Sort the data in ascending order

First, we sort the given data: \(20,29,32,32,33,34,35,36,37,37,38,38,41,42,42,42,43,44,45,47,47,48,49,52,52,54,55,56,64,65,67,68\)

Step2: Determine the stems and leaves

The stems are the tens - digit of the numbers. For example, for the number \(20\), the stem is \(2\) and the leaf is \(0\); for the number \(29\), the stem is \(2\) and the leaf is \(9\); for the number \(32\), the stem is \(3\) and the leaf is \(2\) (when there are two \(32\)s, we list both leaves).

• Stem \(2\): Leaves are \(0,9\)
• Stem \(3\): Leaves are \(2,2,3,4,5,6,7,7,8,8\)
• Stem \(4\): Leaves are \(1,2,2,2,3,4,5,7,7,8,9\)
• Stem \(5\): Leaves are \(2,2,4,5,6\)
• Stem \(6\): Leaves are \(4,5,7,8\)

Answer:

Stem	Leaves
\(3\)	\(2,2,3,4,5,6,7,7,8,8\)
\(4\)	\(1,2,2,2,3,4,5,7,7,8,9\)
\(5\)	\(2,2,4,5,6\)
\(6\)	\(4,5,7,8\)