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:
```
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15 -|
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10 -|
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5 -|
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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.
