Answer :
Certainly! To represent the marks obtained by students in the form of a histogram, we'll follow these steps:
1. Identify the intervals and corresponding frequencies:
We have the marks intervals and the number of students (frequencies) as shown in the table:
- Intervals: [tex]$0-10$[/tex], [tex]$10-20$[/tex], [tex]$20-30$[/tex], [tex]$30-40$[/tex], [tex]$40-50$[/tex], [tex]$50-60$[/tex], [tex]$60-70$[/tex]
- Number of students: 4, 8, 6, 15, 20, 20, 12
2. Set up the axes:
- The horizontal axis (x-axis) will represent the marks intervals.
- The vertical axis (y-axis) will represent the number of students.
3. Construct the bars:
- Each interval will have a corresponding bar whose height represents the number of students in that interval.
- The width of each bar will be uniform and consistent with the intervals (e.g., each interval has a width of 10 marks).
4. Label the axes and give the histogram a title:
- Label the x-axis as "Marks".
- Label the y-axis as "Number of Students".
- Give the histogram a title such as "Marks Distribution of Students".
Let's detail this step-by-step process.
### Step-by-Step Solution:
1. Draw the axes:
- Draw perpendicular axes, the horizontal one being the x-axis (Marks) and the vertical one being the y-axis (Number of Students).
2. Mark the intervals on the x-axis:
- Partition the x-axis into segments representing the intervals: [tex]$0-10$[/tex], [tex]$10-20$[/tex], [tex]$20-30$[/tex], [tex]$30-40$[/tex], [tex]$40-50$[/tex], [tex]$50-60$[/tex], [tex]$60-70$[/tex].
3. Mark the frequencies on the y-axis:
- Choose a scale to represent the number of students. For example, if the highest frequency is 20, a scale of 0 to 25 with an interval of 5 might be appropriate.
4. Draw the bars:
- For each interval, draw a vertical bar whose height corresponds to the number of students in that interval.
Here is a textual representation of how to construct the histogram:
- [tex]$0-10$[/tex] marks: Draw a bar from 0 to 10 (on the x-axis) with a height of 4 (on the y-axis).
- [tex]$10-20$[/tex] marks: Draw a bar from 10 to 20 with a height of 8.
- [tex]$20-30$[/tex] marks: Draw a bar from 20 to 30 with a height of 6.
- [tex]$30-40$[/tex] marks: Draw a bar from 30 to 40 with a height of 15.
- [tex]$40-50$[/tex] marks: Draw a bar from 40 to 50 with a height of 20.
- [tex]$50-60$[/tex] marks: Draw a bar from 50 to 60 with a height of 20.
- [tex]$60-70$[/tex] marks: Draw a bar from 60 to 70 with a height of 12.
### Final Steps:
- Ensure the bars are contiguous (they touch each other since this is a continuous data set on marks).
- Label the x-axis and y-axis appropriately.
- Give the histogram a suitable title.
The resulting histogram will visually represent the distribution of marks among the 90 students in the given intervals. This graphical representation makes it easier to see where most students fall in the marks spectrum and can be used to analyze trends in student performance.
1. Identify the intervals and corresponding frequencies:
We have the marks intervals and the number of students (frequencies) as shown in the table:
- Intervals: [tex]$0-10$[/tex], [tex]$10-20$[/tex], [tex]$20-30$[/tex], [tex]$30-40$[/tex], [tex]$40-50$[/tex], [tex]$50-60$[/tex], [tex]$60-70$[/tex]
- Number of students: 4, 8, 6, 15, 20, 20, 12
2. Set up the axes:
- The horizontal axis (x-axis) will represent the marks intervals.
- The vertical axis (y-axis) will represent the number of students.
3. Construct the bars:
- Each interval will have a corresponding bar whose height represents the number of students in that interval.
- The width of each bar will be uniform and consistent with the intervals (e.g., each interval has a width of 10 marks).
4. Label the axes and give the histogram a title:
- Label the x-axis as "Marks".
- Label the y-axis as "Number of Students".
- Give the histogram a title such as "Marks Distribution of Students".
Let's detail this step-by-step process.
### Step-by-Step Solution:
1. Draw the axes:
- Draw perpendicular axes, the horizontal one being the x-axis (Marks) and the vertical one being the y-axis (Number of Students).
2. Mark the intervals on the x-axis:
- Partition the x-axis into segments representing the intervals: [tex]$0-10$[/tex], [tex]$10-20$[/tex], [tex]$20-30$[/tex], [tex]$30-40$[/tex], [tex]$40-50$[/tex], [tex]$50-60$[/tex], [tex]$60-70$[/tex].
3. Mark the frequencies on the y-axis:
- Choose a scale to represent the number of students. For example, if the highest frequency is 20, a scale of 0 to 25 with an interval of 5 might be appropriate.
4. Draw the bars:
- For each interval, draw a vertical bar whose height corresponds to the number of students in that interval.
Here is a textual representation of how to construct the histogram:
- [tex]$0-10$[/tex] marks: Draw a bar from 0 to 10 (on the x-axis) with a height of 4 (on the y-axis).
- [tex]$10-20$[/tex] marks: Draw a bar from 10 to 20 with a height of 8.
- [tex]$20-30$[/tex] marks: Draw a bar from 20 to 30 with a height of 6.
- [tex]$30-40$[/tex] marks: Draw a bar from 30 to 40 with a height of 15.
- [tex]$40-50$[/tex] marks: Draw a bar from 40 to 50 with a height of 20.
- [tex]$50-60$[/tex] marks: Draw a bar from 50 to 60 with a height of 20.
- [tex]$60-70$[/tex] marks: Draw a bar from 60 to 70 with a height of 12.
### Final Steps:
- Ensure the bars are contiguous (they touch each other since this is a continuous data set on marks).
- Label the x-axis and y-axis appropriately.
- Give the histogram a suitable title.
The resulting histogram will visually represent the distribution of marks among the 90 students in the given intervals. This graphical representation makes it easier to see where most students fall in the marks spectrum and can be used to analyze trends in student performance.
