Sure! Here is the step-by-step solution to draw a histogram and frequency polygon for the given data:
### Histogram
1. Understand the Given Data:
- The percentage ranges and corresponding frequencies are:
- 0-9: 1
- 10-19: 2
- 20-29: 5
- 30-39: 17
- 40-49: 23
- 50-59: 25
- 60-69: 18
- 70-79: 5
- 80-89: 3
- 90-99: 1
2. Label the axes:
- X-axis: Percentage Ranges
- Y-axis: Frequency
3. Draw the Bars:
- Each bar represents the frequency of the corresponding percentage range.
- Heights of the bars correspond to the frequencies.
### Frequency Polygon
1. Calculate the Midpoints of Each Percentage Range:
- The midpoint of each range is calculated as:
[tex]\[
\text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2}
\][/tex]
- For the ranges given:
- 0-9: Midpoint = (0+9)/2 = 4.5
- 10-19: Midpoint = (10+19)/2 = 14.5
- 20-29: Midpoint = (20+29)/2 = 24.5
- 30-39: Midpoint = (30+39)/2 = 34.5
- 40-49: Midpoint = (40+49)/2 = 44.5
- 50-59: Midpoint = (50+59)/2 = 54.5
- 60-69: Midpoint = (60+69)/2 = 64.5
- 70-79: Midpoint = (70+79)/2 = 74.5
- 80-89: Midpoint = (80+89)/2 = 84.5
- 90-99: Midpoint = (90+99)/2 = 94.5
2. Plot the Points:
- Each point on the frequency polygon is plotted using the midpoints on the X-axis and the frequencies on the Y-axis.
3. Connect the Points:
- Draw straight lines to connect the plotted points sequentially.
- To close the polygon, you may start from the midpoints at 0 and 100 with a frequency of 0.
### Example Plotting Instructions
1. Histogram:
- Draw bars with heights corresponding to frequencies at intervals fitting each percentage range.
2. Frequency Polygon:
- Plot (4.5, 1), (14.5, 2), (24.5, 5), (34.5, 17), (44.5, 23), (54.5, 25), (64.5, 18), (74.5, 5), (84.5, 3), (94.5, 1).
- Connect these points and optionally include points (0, 0) and (100, 0) to close the polygon.
### Visual Diagrams
#### Histogram:
```
Frequency |
|
25 | [ ]
| | |
| | | [ ]
| | | | |
20 | | | | |
| | | | | [ ]
| | | | | | |
15 | | | | | | |
| | | | | | |
10 | | | | | | |
| | | | | | |
| | | | | [ ] | |
5 | [ ] | | [ ] | | | | | |
| | | | | | | | | | | | |
| | | | | | | | | | | | |
|__________________________________________________________
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
```
#### Frequency Polygon:
```
Frequency |
|
25 |
| /|\
20 | / \
| / |
15 | / \ |
| / \ |
10 | / |
| / |
5 | /
| /
0 __________________________________________________
0 4.5 14.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5 (Midpoints)
```
Following these steps should help in creating both the histogram and the frequency polygon accurately.
