Question

a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages: 69, 47, 44, 48, 35, 56, 42, 45, 45, 23, 58, 66, 54, 42, 61, 60, 30, 36, 42, 26, 31, 41, 35, 38, 54, 60, 58, 41, 53, 20, 38, 68, 47, 47, 33, 38, 44, 30, 28, 49. 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 3 4 5 6 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. none of the college professors live to be 70 years old. c. if you are younger than 30, you cannot be a college professor. d. none of the above.

Explanation:

Step1: Organize data for stem - and - leaf plot

First, we group the data by the tens digit (stem) and list the units digit (leaf) for each value.

Step2: Fill in the leaves for each stem

For stem 2: The data values in the 20s are 20, 23, 26, 28. So the leaves are 0, 3, 6, 8.
For stem 3: The data values in the 30s are 30, 30, 31, 33, 35, 36, 38, 38. So the leaves are 0, 0, 1, 3, 5, 6, 8, 8.
For stem 4: The data values in the 40s are 41, 41, 42, 42, 44, 44, 45, 45, 47, 47, 47, 48, 49. So the leaves are 1, 1, 2, 2, 4, 4, 5, 5, 7, 7, 7, 8, 9.
For stem 5: The data values in the 50s are 53, 54, 56, 58, 58. So the leaves are 3, 4, 6, 8, 8.
For stem 6: The data values in the 60s are 60, 60, 61, 66. So the leaves are 0, 0, 1, 6.

Stem | Leaves
---|---
2 | 0 3 6 8
3 | 0 0 1 3 5 6 8 8
4 | 1 1 2 2 4 4 5 5 7 7 7 8 9
5 | 3 4 6 8 8
6 | 0 0 1 6

Step3: Analyze the shape of the distribution

Looking at the stem - and - leaf plot, we can see that the data is somewhat symmetric around the middle values (40s). There are no extreme outliers.

Answer:

a. Stem | Leaves
---|---
2 | 0 3 6 8
3 | 0 0 1 3 5 6 8 8
4 | 1 1 2 2 4 4 5 5 7 7 7 8 9
5 | 3 4 6 8 8
6 | 0 0 1 6

b. The shape of the display reveals that the data is somewhat symmetric around the middle values (ages in the 40s), with no extreme outliers.