Answer :
To complete the frequency table and create a histogram, let's follow these steps:
### Step-by-Step Solution:
1. Recording the Ages:
- The ages of the riders are: 47, 16, 16, 35, 45, 43, 11, 29, 31, 50, 23, 18, 18, 20, 29, 17, 18, 48, 56, 24, 18, 21, 38, 12, 23.
2. Identify Intervals for Frequency Table:
- The intervals are:
- 10-19
- 20-29
- 30-39
- 40-49
- 50-59
3. Counting the Ages in Each Interval:
- Interval 10-19:
- Ages: 16, 16, 11, 18, 18, 17, 18, 12, 18
- Frequency: 9
- Interval 20-29:
- Ages: 29, 23, 20, 29, 24, 21, 23
- Frequency: 7
- Interval 30-39:
- Ages: 35, 31, 38
- Frequency: 3
- Interval 40-49:
- Ages: 47, 45, 43, 48
- Frequency: 4
- Interval 50-59:
- Ages: 50, 56
- Frequency: 2
4. Filling the Frequency Table:
\begin{tabular}{|c|c|}
\hline Interval & Frequency \\
\hline [tex]$10-19$[/tex] & 9 \\
\hline [tex]$20-29$[/tex] & 7 \\
\hline [tex]$30-39$[/tex] & 3 \\
\hline [tex]$40-49$[/tex] & 4 \\
\hline [tex]$50-59$[/tex] & 2 \\
\hline
\end{tabular}
5. Creating the Histogram:
On the x-axis, we have the intervals:
- 10-19
- 20-29
- 30-39
- 40-49
- 50-59
On the y-axis, we have the frequency of riders in each interval:
- 0 to 10 (as the maximum frequency is 9)
The bars of the histogram will represent the frequency for each interval.
```
Frequency
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
+-------------------
10 20 30 40 50
-19 -29 -39 -49 -59
```
### Analysis:
1. Most Common Age Group:
- The age group 10-19 years has the highest number of riders (9 riders). This means that teenagers and younger riders are the most frequent riders on the roller coaster during this fifteen-minute period.
2. Diverse Range of Ages:
- The data shows that people of all ages enjoy the roller coaster, from as young as 10 to those in their late 50s.
- The frequencies spread across all intervals, indicating a broad interest in the roller coaster among different age groups.
### Step-by-Step Solution:
1. Recording the Ages:
- The ages of the riders are: 47, 16, 16, 35, 45, 43, 11, 29, 31, 50, 23, 18, 18, 20, 29, 17, 18, 48, 56, 24, 18, 21, 38, 12, 23.
2. Identify Intervals for Frequency Table:
- The intervals are:
- 10-19
- 20-29
- 30-39
- 40-49
- 50-59
3. Counting the Ages in Each Interval:
- Interval 10-19:
- Ages: 16, 16, 11, 18, 18, 17, 18, 12, 18
- Frequency: 9
- Interval 20-29:
- Ages: 29, 23, 20, 29, 24, 21, 23
- Frequency: 7
- Interval 30-39:
- Ages: 35, 31, 38
- Frequency: 3
- Interval 40-49:
- Ages: 47, 45, 43, 48
- Frequency: 4
- Interval 50-59:
- Ages: 50, 56
- Frequency: 2
4. Filling the Frequency Table:
\begin{tabular}{|c|c|}
\hline Interval & Frequency \\
\hline [tex]$10-19$[/tex] & 9 \\
\hline [tex]$20-29$[/tex] & 7 \\
\hline [tex]$30-39$[/tex] & 3 \\
\hline [tex]$40-49$[/tex] & 4 \\
\hline [tex]$50-59$[/tex] & 2 \\
\hline
\end{tabular}
5. Creating the Histogram:
On the x-axis, we have the intervals:
- 10-19
- 20-29
- 30-39
- 40-49
- 50-59
On the y-axis, we have the frequency of riders in each interval:
- 0 to 10 (as the maximum frequency is 9)
The bars of the histogram will represent the frequency for each interval.
```
Frequency
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
+-------------------
10 20 30 40 50
-19 -29 -39 -49 -59
```
### Analysis:
1. Most Common Age Group:
- The age group 10-19 years has the highest number of riders (9 riders). This means that teenagers and younger riders are the most frequent riders on the roller coaster during this fifteen-minute period.
2. Diverse Range of Ages:
- The data shows that people of all ages enjoy the roller coaster, from as young as 10 to those in their late 50s.
- The frequencies spread across all intervals, indicating a broad interest in the roller coaster among different age groups.
