Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages.
68, 49, 47, 45, 30, 58, 49, 47, 41, 20, 55, 68, 57, 48, 64,
65, 56, 41, 58, 26, 32, 67, 41, 49, 30, 38, 45, 35, 28, 43,
64, 32, 31, 43, 24, 33, 44, 32, 34, 52.
construct a stem - and - leaf plot for the data. complete parts a. and b.

Explanation:

Step1: Identify the stems

The stems are the tens - digit of the ages. For the given data, the stems are \(2\), \(3\), \(4\), \(5\), \(6\).

Step2: Identify the leaves

The leaves are the units - digit of the ages.

• For stem \(2\): The ages with tens - digit \(2\) are \(20\), \(24\), \(26\), \(28\), so the leaves are \(0\), \(4\), \(6\), \(8\).
• For stem \(3\): The ages with tens - digit \(3\) are \(30\), \(30\), \(31\), \(32\), \(32\), \(32\), \(33\), \(34\), \(35\), \(38\), so the leaves are \(0\), \(0\), \(1\), \(2\), \(2\), \(2\), \(3\), \(4\), \(5\), \(8\).
• For stem \(4\): The ages with tens - digit \(4\) are \(41\), \(41\), \(41\), \(43\), \(43\), \(44\), \(45\), \(45\), \(47\), \(47\), \(48\), \(49\), \(49\), \(49\), so the leaves are \(1\), \(1\), \(1\), \(3\), \(3\), \(4\), \(5\), \(5\), \(7\), \(7\), \(8\), \(9\), \(9\), \(9\).
• For stem \(5\): The ages with tens - digit \(5\) are \(52\), \(55\), \(56\), \(57\), \(58\), \(58\), so the leaves are \(2\), \(5\), \(6\), \(7\), \(8\), \(8\).
• For stem \(6\): The ages with tens - digit \(6\) are \(64\), \(64\), \(65\), \(67\), \(68\), \(68\), so the leaves are \(4\), \(4\), \(5\), \(7\), \(8\), \(8\).

Answer:

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