Answer :
We begin by listing the temperature readings from the 24 patients. The values given are
[tex]$$
\begin{array}{cccccc}
98.8 & 98.2 & 98.6 & 98.4 & 98.8 & 98.6 \\
98.3 & 98.8 & 98.5 & 98.6 & 98.6 & 98.5 \\
98.4 & 98.6 & 98.7 & 98.6 & 98.1 & 98.2 \\
98.6 & 98.7 & 98.4 & 98.7 & 98.0 & 98.4 \\
\end{array}
$$[/tex]
### Step 1. Count the Frequencies
List the unique temperature values in order and count how many times each occurs:
1. [tex]$98.0$[/tex]: appears 1 time.
2. [tex]$98.1$[/tex]: appears 1 time.
3. [tex]$98.2$[/tex]: appears 2 times.
4. [tex]$98.3$[/tex]: appears 1 time.
5. [tex]$98.4$[/tex]: appears 4 times.
6. [tex]$98.5$[/tex]: appears 2 times.
7. [tex]$98.6$[/tex]: appears 7 times.
8. [tex]$98.7$[/tex]: appears 3 times.
9. [tex]$98.8$[/tex]: appears 3 times.
A quick verification shows that
[tex]$$1 + 1 + 2 + 1 + 4 + 2 + 7 + 3 + 3 = 24,$$[/tex]
which confirms that all 24 readings are accounted for.
### Step 2. Construct the Dot Plot
In a dot plot, each unique temperature is marked on the horizontal (x-) axis, and dots are stacked vertically above each value corresponding to their frequency.
Below is a representation of the dot plot (each “[tex]$\bullet$[/tex]” represents one patient’s temperature):
- [tex]$98.0$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.1$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.2$[/tex]: [tex]$\bullet \; \bullet$[/tex]
- [tex]$98.3$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.4$[/tex]: [tex]$\bullet \; \bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.5$[/tex]: [tex]$\bullet \; \bullet$[/tex]
- [tex]$98.6$[/tex]: [tex]$\bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.7$[/tex]: [tex]$\bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.8$[/tex]: [tex]$\bullet \; \bullet \; \bullet$[/tex]
### Step 3. Plot Explanation
1. Draw a horizontal number line. Mark the points [tex]$98.0, 98.1, 98.2, 98.3, 98.4, 98.5, 98.6, 98.7$[/tex], and [tex]$98.8$[/tex].
2. For each temperature value, stack as many dots vertically as its frequency.
- For example, for [tex]$98.6$[/tex], place 7 dots (one above the other) at the position corresponding to [tex]$98.6$[/tex].
3. Label the [tex]$x$[/tex]-axis as “Temperature ([tex]$^\circ\text{F}$[/tex])” and the [tex]$y$[/tex]-axis as “Frequency.”
This dot plot clearly visualizes the temperature distribution among the patients in Ward B.
### Final Answer
The dot plot for the temperature data is as follows:
[tex]$$
\begin{array}{rcl}
\textbf{Temperature (in }^\circ\text{F}\textbf{)} & \qquad & \textbf{Dots (Frequency)} \\
98.0 & : & \bullet \\
98.1 & : & \bullet \\
98.2 & : & \bullet \quad \bullet \\
98.3 & : & \bullet \\
98.4 & : & \bullet \quad \bullet \quad \bullet \quad \bullet \\
98.5 & : & \bullet \quad \bullet \\
98.6 & : & \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \\
98.7 & : & \bullet \quad \bullet \quad \bullet \\
98.8 & : & \bullet \quad \bullet \quad \bullet \\
\end{array}
$$[/tex]
This completes the construction of the dot plot.
[tex]$$
\begin{array}{cccccc}
98.8 & 98.2 & 98.6 & 98.4 & 98.8 & 98.6 \\
98.3 & 98.8 & 98.5 & 98.6 & 98.6 & 98.5 \\
98.4 & 98.6 & 98.7 & 98.6 & 98.1 & 98.2 \\
98.6 & 98.7 & 98.4 & 98.7 & 98.0 & 98.4 \\
\end{array}
$$[/tex]
### Step 1. Count the Frequencies
List the unique temperature values in order and count how many times each occurs:
1. [tex]$98.0$[/tex]: appears 1 time.
2. [tex]$98.1$[/tex]: appears 1 time.
3. [tex]$98.2$[/tex]: appears 2 times.
4. [tex]$98.3$[/tex]: appears 1 time.
5. [tex]$98.4$[/tex]: appears 4 times.
6. [tex]$98.5$[/tex]: appears 2 times.
7. [tex]$98.6$[/tex]: appears 7 times.
8. [tex]$98.7$[/tex]: appears 3 times.
9. [tex]$98.8$[/tex]: appears 3 times.
A quick verification shows that
[tex]$$1 + 1 + 2 + 1 + 4 + 2 + 7 + 3 + 3 = 24,$$[/tex]
which confirms that all 24 readings are accounted for.
### Step 2. Construct the Dot Plot
In a dot plot, each unique temperature is marked on the horizontal (x-) axis, and dots are stacked vertically above each value corresponding to their frequency.
Below is a representation of the dot plot (each “[tex]$\bullet$[/tex]” represents one patient’s temperature):
- [tex]$98.0$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.1$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.2$[/tex]: [tex]$\bullet \; \bullet$[/tex]
- [tex]$98.3$[/tex]: [tex]$\bullet$[/tex]
- [tex]$98.4$[/tex]: [tex]$\bullet \; \bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.5$[/tex]: [tex]$\bullet \; \bullet$[/tex]
- [tex]$98.6$[/tex]: [tex]$\bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.7$[/tex]: [tex]$\bullet \; \bullet \; \bullet$[/tex]
- [tex]$98.8$[/tex]: [tex]$\bullet \; \bullet \; \bullet$[/tex]
### Step 3. Plot Explanation
1. Draw a horizontal number line. Mark the points [tex]$98.0, 98.1, 98.2, 98.3, 98.4, 98.5, 98.6, 98.7$[/tex], and [tex]$98.8$[/tex].
2. For each temperature value, stack as many dots vertically as its frequency.
- For example, for [tex]$98.6$[/tex], place 7 dots (one above the other) at the position corresponding to [tex]$98.6$[/tex].
3. Label the [tex]$x$[/tex]-axis as “Temperature ([tex]$^\circ\text{F}$[/tex])” and the [tex]$y$[/tex]-axis as “Frequency.”
This dot plot clearly visualizes the temperature distribution among the patients in Ward B.
### Final Answer
The dot plot for the temperature data is as follows:
[tex]$$
\begin{array}{rcl}
\textbf{Temperature (in }^\circ\text{F}\textbf{)} & \qquad & \textbf{Dots (Frequency)} \\
98.0 & : & \bullet \\
98.1 & : & \bullet \\
98.2 & : & \bullet \quad \bullet \\
98.3 & : & \bullet \\
98.4 & : & \bullet \quad \bullet \quad \bullet \quad \bullet \\
98.5 & : & \bullet \quad \bullet \\
98.6 & : & \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \quad \bullet \\
98.7 & : & \bullet \quad \bullet \quad \bullet \\
98.8 & : & \bullet \quad \bullet \quad \bullet \\
\end{array}
$$[/tex]
This completes the construction of the dot plot.
