To correctly graph the given data set [tex]\(\{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3\}\)[/tex] into a stem-and-leaf plot, we need to organize the numbers by their tens (stems) and units (leaves). Here's how you can do it:
1. Split each number into its stem and leaf:
- 0 -> Stem: 0, Leaf: 0
- 3 -> Stem: 0, Leaf: 3
- 11 -> Stem: 1, Leaf: 1
- 17 -> Stem: 1, Leaf: 7
- 17 -> Stem: 1, Leaf: 7
- 17 -> Stem: 1, Leaf: 7
- 17 -> Stem: 1, Leaf: 7
- 20 -> Stem: 2, Leaf: 0
- 20 -> Stem: 2, Leaf: 0
- 20 -> Stem: 2, Leaf: 0
- 22 -> Stem: 2, Leaf: 2
- 24 -> Stem: 2, Leaf: 4
- 28 -> Stem: 2, Leaf: 8
- 28 -> Stem: 2, Leaf: 8
- 31 -> Stem: 3, Leaf: 1
- 33 -> Stem: 3, Leaf: 3
2. Organize the data into stems and their corresponding leaves:
- For stem 0, the leaves are [0, 3].
- For stem 1, the leaves are [1, 7, 7, 7, 7].
- For stem 2, the leaves are [0, 0, 0, 2, 4, 8, 8].
- For stem 3, the leaves are [1, 3].
3. Construct the stem-and-leaf plot in a tabular format:
[tex]\[
\begin{array}{l|l}
\multicolumn{2}{l}{\text{2021 Riverside Red Dragon Football Season Points}} \\
\hline
0 & 03 \\
1 & 17777 \\
2 & 0002488 \\
3 & 13 \\
\end{array}
\][/tex]
This stem-and-leaf plot correctly represents the given data set. Here's why:
- Stem 0: Leaves are 0, 3 => 03
- Stem 1: Leaves are 1, 7, 7, 7, 7 => 17777
- Stem 2: Leaves are 0, 0, 0, 2, 4, 8, 8 => 0002488
- Stem 3: Leaves are 1, 3 => 13
Thus, the correct stem-and-leaf plot for the provided data set is:
[tex]\[
\begin{tabular}{l|l}
\multicolumn{2}{l}{Season Points} \\
\hline 0 & 03 \\
1 & 17777 \\
2 & 0002488 \\
3 & 13 \\
\end{tabular}
\][/tex]
