To construct a stem-and-leaf diagram for the given data, follow these steps:
1. Identify the Stems and Leaves:
- The stem consists of all but the last digit of each number, while the leaf is the last digit of each number.
- Example: For the age 33, the stem is 3, and the leaf is 3.
2. List the Ages Given:
- 33, 48, 66, 21, 62, 68, 73, 61, 55, 23, 39, 47, 78, 64, 49, 50, 34, 36, 45, 48, 51, 51, 28, 43, 44, 52, 52, 34.
3. Sort Ages into Stems and Leaves:
- For stem 2 (20-29): The leaves would be 1, 3, and 8.
- For stem 3 (30-39): The leaves would be 3, 4, 4, 6, and 9.
- For stem 4 (40-49): The leaves would be 3, 4, 5, 7, 8, 8, and 9.
- For stem 5 (50-59): The leaves would be 0, 1, 1, 2, 2, and 5.
- For stem 6 (60-69): The leaves would be 1, 2, 4, 6, and 8.
- For stem 7 (70-79): The leaves would be 3 and 8.
4. Arrange the Leaves in Ascending Order for Each Stem:
- Stem 2: Leaves: 1, 3, 8
- Stem 3: Leaves: 3, 4, 4, 6, 9
- Stem 4: Leaves: 3, 4, 5, 7, 8, 8, 9
- Stem 5: Leaves: 0, 1, 1, 2, 2, 5
- Stem 6: Leaves: 1, 2, 4, 6, 8
- Stem 7: Leaves: 3, 8
5. Construct the Stem-and-Leaf Diagram:
[tex]\[
\begin{array}{|c|l|}
\hline \text{Stems} & \text{Leaves} \\
\hline
2 & 1 \ 3 \ 8 \\
3 & 3 \ 4 \ 4 \ 6 \ 9 \\
4 & 3 \ 4 \ 5 \ 7 \ 8 \ 8 \ 9 \\
5 & 0 \ 1 \ 1 \ 2 \ 2 \ 5 \\
6 & 1 \ 2 \ 4 \ 6 \ 8 \\
7 & 3 \ 8 \\
\hline
\end{array}
\][/tex]
This table represents a stem-and-leaf plot where each stem represents the tens place of the ages, and each leaf represents the units place of the ages listed under the corresponding stem. This diagram helps to visualize the distribution of ages among the customers who purchased a cruise.
