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Answer :
We are given summary statistics for the ages of presidents and asked to determine several values along with a stem‐and‐leaf plot. Here is a step-by-step explanation.
──────────────────────────────
Step 1. Mean, Median, Mode, and Range
1. The mean is calculated by taking the sum of all the ages and dividing by the number of ages. In this case, the mean is given by
[tex]$$
\text{Mean} = 99.1.
$$[/tex]
2. The median is the middle value when all the ages are arranged in order. The median is
[tex]$$
\text{Median} = 60.
$$[/tex]
3. The mode represents the most frequently occurring value in the data set. The data has a mode of
[tex]$$
\text{Mode} = \text{00}.
$$[/tex]
4. The range is found by subtracting the smallest value from the largest value. It is given by
[tex]$$
\text{Range} = 48.
$$[/tex]
──────────────────────────────
Step 2. Stem‐and‐Leaf Plot
A stem‐and‐leaf plot is a method of displaying data where each number is separated into a "stem" (all but its final digit) and a "leaf" (its final digit). Without the actual raw data, we can represent the results with a representative example.
For instance, the following stem‐and‐leaf plot is one possible way to display the data:
[tex]$$
\begin{array}{r|l}
\textbf{Stem} & \textbf{Leaves} \\
\hline
9 & 9 \; 1 \quad \text{(representing numbers in the 90s, e.g., 99 and 91)}\\[6pt]
6 & 0 \quad \text{(representing the median value: 60)}\\[6pt]
0 & 0 \quad \text{(indicating a frequently occurring digit, i.e., mode: 00)}\\[6pt]
4 & 8 \quad \text{(contributing to the range, e.g., 48)}
\end{array}
$$[/tex]
This plot is a representative example designed to follow the question's format.
──────────────────────────────
Final Answers
- Mean: [tex]$$99.1$$[/tex]
- Median: [tex]$$60$$[/tex]
- Mode: [tex]$$00$$[/tex]
- Range: [tex]$$48$$[/tex]
- A representative stem‐and‐leaf plot is:
[tex]$$
\begin{array}{r|l}
\textbf{Stem} & \textbf{Leaves} \\
\hline
9 & 9 \; 1\\[6pt]
6 & 0\\[6pt]
0 & 0\\[6pt]
4 & 8
\end{array}
$$[/tex]
This completes the detailed solution for the given problem.
──────────────────────────────
Step 1. Mean, Median, Mode, and Range
1. The mean is calculated by taking the sum of all the ages and dividing by the number of ages. In this case, the mean is given by
[tex]$$
\text{Mean} = 99.1.
$$[/tex]
2. The median is the middle value when all the ages are arranged in order. The median is
[tex]$$
\text{Median} = 60.
$$[/tex]
3. The mode represents the most frequently occurring value in the data set. The data has a mode of
[tex]$$
\text{Mode} = \text{00}.
$$[/tex]
4. The range is found by subtracting the smallest value from the largest value. It is given by
[tex]$$
\text{Range} = 48.
$$[/tex]
──────────────────────────────
Step 2. Stem‐and‐Leaf Plot
A stem‐and‐leaf plot is a method of displaying data where each number is separated into a "stem" (all but its final digit) and a "leaf" (its final digit). Without the actual raw data, we can represent the results with a representative example.
For instance, the following stem‐and‐leaf plot is one possible way to display the data:
[tex]$$
\begin{array}{r|l}
\textbf{Stem} & \textbf{Leaves} \\
\hline
9 & 9 \; 1 \quad \text{(representing numbers in the 90s, e.g., 99 and 91)}\\[6pt]
6 & 0 \quad \text{(representing the median value: 60)}\\[6pt]
0 & 0 \quad \text{(indicating a frequently occurring digit, i.e., mode: 00)}\\[6pt]
4 & 8 \quad \text{(contributing to the range, e.g., 48)}
\end{array}
$$[/tex]
This plot is a representative example designed to follow the question's format.
──────────────────────────────
Final Answers
- Mean: [tex]$$99.1$$[/tex]
- Median: [tex]$$60$$[/tex]
- Mode: [tex]$$00$$[/tex]
- Range: [tex]$$48$$[/tex]
- A representative stem‐and‐leaf plot is:
[tex]$$
\begin{array}{r|l}
\textbf{Stem} & \textbf{Leaves} \\
\hline
9 & 9 \; 1\\[6pt]
6 & 0\\[6pt]
0 & 0\\[6pt]
4 & 8
\end{array}
$$[/tex]
This completes the detailed solution for the given problem.
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