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, 47, 30, 50, 45, 48, 45, 22, 53, 63, 53, 44, 68,
69, 53, 40, 59, 27, 36, 65, 44, 44, 34, 30, 42, 37, 20, 44,
68, 37, 30, 43, 29, 39, 45, 33, 37, 54.
construct a stem - and - leaf plot for the data. complete parts a. and b.
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. 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: Organize data for stem - and - leaf plot

For the stem - and - leaf plot, the tens digit is the stem and the units digit is the leaf.
For stem 2: The data values starting with 2 are 22, 27, 20. So the leaves are 0, 2, 7.
For stem 3: The data values starting with 3 are 30, 36, 34, 30, 37, 30, 33, 37. So the leaves are 0, 0, 0, 3, 4, 6, 7, 7.
For stem 4: The data values starting with 4 are 44, 47, 45, 48, 45, 44, 44, 44, 42, 43, 45. So the leaves are 2, 3, 4, 4, 4, 4, 5, 5, 7, 8.
For stem 5: The data values starting with 5 are 50, 53, 53, 59, 54. So the leaves are 0, 3, 3, 4, 9.
For stem 6: The data values starting with 6 are 69, 63, 68, 69, 68. So the leaves are 3, 8, 8, 9, 9.

Step2: Analyze the shape of the plot

Count the number of data points in each stem. The stem 4 has the most number of leaves (10 leaves). This means the greatest number of college professors are in their 40s.

Answer:

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