Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages. 61, 48, 44, 43, 31, 57, 43, 49, 46, 28, 58, 66, 54, 40, 69, 65, 53, 42, 50, 21, 31, 65, 44, 48, 34, 37, 48, 35, 24, 47, 63, 36, 33, 48, 21, 31, 46, 33, 30, 54. construct a stem - and - leaf plot for the data. complete parts a. and b. b. what does the shape of the display reveal about the ages of the professors? a. the greatest number of college professors are in their 40s. b. if you are younger than 30, you cannot be a college professor. c. none of the college professors live to be 70 years old. d. none of the above.

Explanation:

Step1: Identify the stems

The stems are the tens - digit of the ages.

Step2: List the leaves

For stem 2: The ages with 2 as the tens - digit are 21, 21, 24, 28. So the leaves are 1 1 4 8.
For stem 3: The ages with 3 as the tens - digit are 30, 31, 31, 31, 33, 33, 34, 35, 36, 37. So the leaves are 0 1 1 1 3 3 4 5 6 7.
For stem 4: The ages with 4 as the tens - digit are 40, 40, 42, 43, 43, 44, 44, 46, 46, 47, 48, 48, 48, 48, 49. So the leaves are 0 0 2 3 3 4 4 6 6 7 8 8 8 8 9.
For stem 5: The ages with 5 as the tens - digit are 50, 53, 54, 54, 57, 58. So the leaves are 0 3 4 4 7 8.
For stem 6: The ages with 6 as the tens - digit are 61, 63, 65, 65, 66, 69. So the leaves are 1 3 5 5 6 9.

Step3: Analyze the shape of the display

Count the number of data points in each stem. The stem 4 has the most number of leaves. This means the greatest number of college professors are in their 40s.

Answer:

Stem | Leaves
--- | ---
2 | 1 1 4 8
3 | 0 1 1 1 3 3 4 5 6 7
4 | 0 0 2 3 3 4 4 6 6 7 8 8 8 8 9
5 | 0 3 4 4 7 8
6 | 1 3 5 5 6 9
A. The greatest number of college professors are in their 40s.