ebunoluwam2
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

The percentage marks of 100 students in a Senior School Certificate examination are grouped as follows:

[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Percentage & $0-9$ & $10-19$ & $20-29$ & $30-39$ & $40-49$ \\
\hline
Frequency & 1 & 2 & 5 & 17 & 23 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Percentage & $50-59$ & $60-69$ & $70-79$ & $80-89$ & $90-99$ \\
\hline
Frequency & 25 & 18 & 5 & 3 & 1 \\
\hline
\end{tabular}
\][/tex]

Draw a histogram and a frequency polygon of the distribution.

Sagot :

GinnyAnswer
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.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.