Which stem-and-leaf plot represents the data set below? 109, 60, 77, 54, 63, 84, 93, 65, 58, 97, 113
6 | 0
5 | 4 8
6 | 3 5
7 | 7
8 | 4
9 | 3 7
1 | 0 1 3
To create a stem-and-leaf plot for the given data set, we need to separate each number into its "stem" and "leaf" components. The stem is the tens digit, and the leaf is the ones digit.
Here's how to create the stem-and-leaf plot for the given data set:
Step 1: Determine the range of the data set. The smallest number is 54, and the largest number is 113. Therefore, the range is 113 - 54 = 59.
Step 2: Decide on the number of stems. Typically, it is a good idea to have around 5 to 10 stems, depending on the range. In this case, let's use 5 stems to start.
Step 3: Write the stems in ascending order. Based on the range of 59 and the number of stems (5), we can write down the stems as follows: 5, 6, 7, 8, 9.
Step 4: Assign the leaves to each stem. Take each number in the data set and separate the tens digit (stem) from the ones digit (leaf).
Now let's assign the leaves to each stem:
Stem 5: 4
Stem 6: 0 3 5 8
Stem 7: 7 7
Stem 8: 4
Stem 9: 3 7
Step 5: List the stems and leaves in a vertical format.
Here is the completed stem-and-leaf plot for the given data set:
\[
\begin{array}{|c|c|}
\hline
5 & 4 \\
\hline
6 & 0\ 3\ 5\ 8 \\
\hline
7 & 7\ 7 \\
\hline
8 & 4 \\
\hline
9 & 3\ 7 \\
\hline
\end{array}
\]
Therefore, the stem-and-leaf plot that represents the data set is:
\[
\begin{align*}
&5\text{ |}\ 4 \\
&6\text{ |}\ 0\ 3\ 5\ 8 \\
&7\text{ |}\ 7\ 7 \\
&8\text{ |}\ 4 \\
&9\text{ |}\ 3\ 7 \\
\end{align*}
\]