Certainly! A stem plot (also known as a stem-and-leaf plot) is a way of displaying data where each data point is split into a "stem" (the leading digit or digits) and a "leaf" (the trailing digit). For the dataset given, we will construct the stem plot in a step-by-step manner:
### Dataset:
71, 38, 52, 47, 55, 53, 76, 65, 77, 63, 65, 63, 68,
54, 64, 62, 87, 47, 64, 56, 78, 64, 58, 51, 91, 74,
71, 41, 67, 62, 106, 46
### Steps:
1. Divide each number into a stem and leaf:
- The "stem" will be the tens place of each number.
- The "leaf" will be the units place of each number.
2. Organize the data:
- Group the leaves with the same stem together.
- Sort the leaves in ascending order within each stem group.
### Stem Plot Construction:
#### Stems and Leaves:
- 3 | 8
- 4 | 1 6 7 7
- 5 | 1 2 3 4 5 6 8
- 6 | 2 2 3 3 4 4 4 5 5 7 8
- 7 | 1 1 4 6 7 8
- 8 | 7
- 9 | 1
- 10| 6
### Stem Plot:
[tex]\[
\begin{array}{c|l}
\text{Stem} & \text{Leaves} \\
\hline
3 & 8 \\
4 & 1, 6, 7, 7 \\
5 & 1, 2, 3, 4, 5, 6, 8 \\
6 & 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8 \\
7 & 1, 1, 4, 6, 7, 8 \\
8 & 7 \\
9 & 1 \\
10 & 6 \\
\\
\end{array}
\][/tex]
[tex]\[
\text{Key: } 4 \,|\, 1 \,=\, 41 \text{ points}
\][/tex]
### Explanation:
- The stem represents the tens place of the numbers.
- The leaf represents the ones place of the numbers.
- For example, the entry `4 | 6 7 7` means 46, 47, 47 points scored, respectively.
This stem plot effectively organizes and visualizes the distribution of points scored by the teams in a clear and concise manner.
