To compare exact times recorded in several attempts of a 20-yard dash, we can use a stem-and-leaf plot. This type of plot is an effective way to organize and display the data to see each time precisely while maintaining the numerical order.
Given the times recorded in the eight 20-yard dash attempts:
[tex]$[tex]$3.5, 2.9, 2.9, 3.4, 3.0, 2.8, 3.1, 2.8$[/tex]$[/tex]
We can create a stem-and-leaf plot as follows:
### Step-by-Step Solution:
1. Identify the stems and leaves:
- The `stem` consists of the integer part of the recorded times.
- The `leaf` consists of the decimal part of the recorded times.
2. List the times:
- The times can be listed as pairs of (stem, leaf) values:
[tex]\[
(3, 5), (2, 9), (2, 9), (3, 4), (3, 0), (2, 8), (3, 1), (2, 8)
\][/tex]
3. Organize the pairs into the stem-and-leaf format:
- Separate times with the same stems into one group while listing their leaves in ascending order:
- Stems and corresponding leaves:
[tex]\[
\begin{array}{c|l}
\text{Stem} & \text{Leaves} \\
\hline
2 & 8, 8, 9, 9 \\
3 & 0, 1, 4, 5 \\
\end{array}
\][/tex]
4. Construct the stem-and-leaf plot:
- Align the stems in a column and list the leaves to the right of the stems.
- The leaves are listed in ascending order for each stem.
The resulting stem-and-leaf plot is shown in the table below:
[tex]\[
\begin{array}{c|llll}
\text{Stem} & \text{Leaf} \\
\hline
2 & 8 & 8 & 9 & 9 \\
3 & 0 & 1 & 4 & 5 \\
\end{array}
\][/tex]
5. Key for understanding:
- To make the stem-and-leaf plot clear to the reader, a key is provided. The key indicates how to interpret the stems and leaves:
- For example, the key "3 | 1 = 3.1" shows that a stem of 3 and a leaf of 1 represent the time 3.1 seconds.
#### Key:
[tex]\[
3 \mid 1 = 3.1
\][/tex]
### Conclusion:
A stem-and-leaf plot is well-suited for comparing exact times recorded in the 20-yard dash attempts, as it allows us to see each individual time while easily identifying patterns and distribution of the data.
