Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To draw a histogram for the given data, follow these steps:
1. Understand the Class Intervals and Frequencies:
The data provided is:
- Class Intervals (Marks): [tex]\(0-10, 10-20, 20-30, 30-40, 40-50\)[/tex]
- Frequencies (No. of Students): [tex]\(2, 5, 15, 10, 8\)[/tex]
2. Determine the Midpoints of Each Class Interval:
The midpoints are calculated as the average of the lower and upper bounds of each interval.
- Midpoint of [tex]\(0-10\)[/tex] is [tex]\((0 + 10) / 2 = 5\)[/tex]
- Midpoint of [tex]\(10-20\)[/tex] is [tex]\((10 + 20) / 2 = 15\)[/tex]
- Midpoint of [tex]\(20-30\)[/tex] is [tex]\((20 + 30) / 2 = 25\)[/tex]
- Midpoint of [tex]\(30-40\)[/tex] is [tex]\((30 + 40) / 2 = 35\)[/tex]
- Midpoint of [tex]\(40-50\)[/tex] is [tex]\((40 + 50) / 2 = 45\)[/tex]
These midpoints will serve as our x-values for plotting the histogram.
3. Plot the Histogram:
To plot the histogram, you need to represent the class intervals on the x-axis and the number of students on the y-axis. For each class interval, draw a bar with a height equal to the number of students in that interval.
For a detailed, step-by-step manual drawing:
- Draw the x-axis and y-axis on your graph paper or graphing tool.
- Label the x-axis with the class intervals [tex]\(0-10, 10-20, 20-30, 30-40, 40-50\)[/tex].
- Label the y-axis with appropriate scale values corresponding to the number of students, such as 0 to 15.
- For the interval [tex]\(0-10\)[/tex], draw a bar from 0 to 10 with a height of 2 units.
- For the interval [tex]\(10-20\)[/tex], draw a bar from 10 to 20 with a height of 5 units.
- For the interval [tex]\(20-30\)[/tex], draw a bar from 20 to 30 with a height of 15 units.
- For the interval [tex]\(30-40\)[/tex], draw a bar from 30 to 40 with a height of 10 units.
- For the interval [tex]\(40-50\)[/tex], draw a bar from 40 to 50 with a height of 8 units.
4. Add Titles and Labels:
- Title the graph as "Histogram of Marks."
- Label the x-axis as "Marks."
- Label the y-axis as "Number of Students."
### Example Visualization:
```
|
|
|
|
15 -|
|
|
|
10 -|
|
|
|
5 -|
|
|
|
0 -|________________________________________
0-10 10-20 20-30 30-40 40-50
```
- The histogram shows clearly marked intervals with bars representing the number of students in each interval.
By following these steps, you will effectively create a histogram that accurately represents the distribution of marks among the 40 students.
1. Understand the Class Intervals and Frequencies:
The data provided is:
- Class Intervals (Marks): [tex]\(0-10, 10-20, 20-30, 30-40, 40-50\)[/tex]
- Frequencies (No. of Students): [tex]\(2, 5, 15, 10, 8\)[/tex]
2. Determine the Midpoints of Each Class Interval:
The midpoints are calculated as the average of the lower and upper bounds of each interval.
- Midpoint of [tex]\(0-10\)[/tex] is [tex]\((0 + 10) / 2 = 5\)[/tex]
- Midpoint of [tex]\(10-20\)[/tex] is [tex]\((10 + 20) / 2 = 15\)[/tex]
- Midpoint of [tex]\(20-30\)[/tex] is [tex]\((20 + 30) / 2 = 25\)[/tex]
- Midpoint of [tex]\(30-40\)[/tex] is [tex]\((30 + 40) / 2 = 35\)[/tex]
- Midpoint of [tex]\(40-50\)[/tex] is [tex]\((40 + 50) / 2 = 45\)[/tex]
These midpoints will serve as our x-values for plotting the histogram.
3. Plot the Histogram:
To plot the histogram, you need to represent the class intervals on the x-axis and the number of students on the y-axis. For each class interval, draw a bar with a height equal to the number of students in that interval.
For a detailed, step-by-step manual drawing:
- Draw the x-axis and y-axis on your graph paper or graphing tool.
- Label the x-axis with the class intervals [tex]\(0-10, 10-20, 20-30, 30-40, 40-50\)[/tex].
- Label the y-axis with appropriate scale values corresponding to the number of students, such as 0 to 15.
- For the interval [tex]\(0-10\)[/tex], draw a bar from 0 to 10 with a height of 2 units.
- For the interval [tex]\(10-20\)[/tex], draw a bar from 10 to 20 with a height of 5 units.
- For the interval [tex]\(20-30\)[/tex], draw a bar from 20 to 30 with a height of 15 units.
- For the interval [tex]\(30-40\)[/tex], draw a bar from 30 to 40 with a height of 10 units.
- For the interval [tex]\(40-50\)[/tex], draw a bar from 40 to 50 with a height of 8 units.
4. Add Titles and Labels:
- Title the graph as "Histogram of Marks."
- Label the x-axis as "Marks."
- Label the y-axis as "Number of Students."
### Example Visualization:
```
|
|
|
|
15 -|
|
|
|
10 -|
|
|
|
5 -|
|
|
|
0 -|________________________________________
0-10 10-20 20-30 30-40 40-50
```
- The histogram shows clearly marked intervals with bars representing the number of students in each interval.
By following these steps, you will effectively create a histogram that accurately represents the distribution of marks among the 40 students.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.