Answer :
To construct a frequency histogram of the given data, follow these steps:
### Step-by-Step Solution
1. Understand the Data:
The data represents the number of students watching TV for different hours ranges:
- [tex]\(0-4\)[/tex] hours: 70 students
- [tex]\(5-9\)[/tex] hours: 90 students
- [tex]\(10-14\)[/tex] hours: 25 students
- [tex]\(15-19\)[/tex] hours: 5 students
2. Choose Suitable Axes:
- The x-axis will represent the ranges of hours of TV watched.
- The y-axis will represent the number of students.
3. Choose an Appropriate Scale:
- For the y-axis, since our highest value is 90, we can choose a scale of 10 units per interval.
- For the x-axis, each bar will represent an interval of hours.
4. Draw the Axes:
- Draw a horizontal line (x-axis) and label it "Hours of TV".
- Draw a vertical line (y-axis) and label it "Number of Students".
5. Label the X-Axis Intervals:
- Mark the intervals [tex]\(0-4\)[/tex], [tex]\(5-9\)[/tex], [tex]\(10-14\)[/tex], and [tex]\(15-19\)[/tex] on the x-axis.
6. Label the Y-Axis:
- Starting from 0 at the origin, mark intervals of 10 up to 100 (to cover from 0 to 90 students).
7. Draw the Bars:
- For each interval on the x-axis, draw a vertical bar up to the corresponding number of students on the y-axis.
- For [tex]\(0-4\)[/tex] hours, draw a bar up to 70.
- For [tex]\(5-9\)[/tex] hours, draw a bar up to 90.
- For [tex]\(10-14\)[/tex] hours, draw a bar up to 25.
- For [tex]\(15-19\)[/tex] hours, draw a bar up to 5.
8. Add a Title:
- Title the histogram: "Frequency Histogram of Hours of TV Watched".
### Constructing the Histogram
Here is a textual representation of what the histogram should look like:
```
^
|
100 |
|
90 | __
| | |
80 | | |
| | |
70 | __ | |
| | | | |
60 | | | | |
| | | | |
50 | | | | |
| | | | |
40 | | | | |
| | | | |
30 | | | | |
| | | | |
20 | | | | |
| | | | |
10 | | | | | __
| | | | | | |
0 |__________|__|____|__|___________|__|__
0-4 5-9 10-14 15-19
Hours of TV
```
### Conclusion
By following these steps, you can effectively create a frequency histogram that visually represents the data on how many hours of TV different numbers of students watch. This histogram helps in understanding the distribution and frequency of students within each range of hours.
### Step-by-Step Solution
1. Understand the Data:
The data represents the number of students watching TV for different hours ranges:
- [tex]\(0-4\)[/tex] hours: 70 students
- [tex]\(5-9\)[/tex] hours: 90 students
- [tex]\(10-14\)[/tex] hours: 25 students
- [tex]\(15-19\)[/tex] hours: 5 students
2. Choose Suitable Axes:
- The x-axis will represent the ranges of hours of TV watched.
- The y-axis will represent the number of students.
3. Choose an Appropriate Scale:
- For the y-axis, since our highest value is 90, we can choose a scale of 10 units per interval.
- For the x-axis, each bar will represent an interval of hours.
4. Draw the Axes:
- Draw a horizontal line (x-axis) and label it "Hours of TV".
- Draw a vertical line (y-axis) and label it "Number of Students".
5. Label the X-Axis Intervals:
- Mark the intervals [tex]\(0-4\)[/tex], [tex]\(5-9\)[/tex], [tex]\(10-14\)[/tex], and [tex]\(15-19\)[/tex] on the x-axis.
6. Label the Y-Axis:
- Starting from 0 at the origin, mark intervals of 10 up to 100 (to cover from 0 to 90 students).
7. Draw the Bars:
- For each interval on the x-axis, draw a vertical bar up to the corresponding number of students on the y-axis.
- For [tex]\(0-4\)[/tex] hours, draw a bar up to 70.
- For [tex]\(5-9\)[/tex] hours, draw a bar up to 90.
- For [tex]\(10-14\)[/tex] hours, draw a bar up to 25.
- For [tex]\(15-19\)[/tex] hours, draw a bar up to 5.
8. Add a Title:
- Title the histogram: "Frequency Histogram of Hours of TV Watched".
### Constructing the Histogram
Here is a textual representation of what the histogram should look like:
```
^
|
100 |
|
90 | __
| | |
80 | | |
| | |
70 | __ | |
| | | | |
60 | | | | |
| | | | |
50 | | | | |
| | | | |
40 | | | | |
| | | | |
30 | | | | |
| | | | |
20 | | | | |
| | | | |
10 | | | | | __
| | | | | | |
0 |__________|__|____|__|___________|__|__
0-4 5-9 10-14 15-19
Hours of TV
```
### Conclusion
By following these steps, you can effectively create a frequency histogram that visually represents the data on how many hours of TV different numbers of students watch. This histogram helps in understanding the distribution and frequency of students within each range of hours.
