Let's analyze the given data step-by-step to understand the solution:
1. Understanding the Data Columns:
- Marks obtained: This column represents the upper bound for a range of marks.
- Number of students: This column represents the cumulative number of students who scored below the respective marks in the first column.
2. Interpreting the Data Table:
- For marks [tex]\(<20\)[/tex], there are 9 students.
- For marks [tex]\(<40\)[/tex], there are 23 students.
- For marks [tex]\(<50\)[/tex], there are 43 students.
- For marks [tex]\(<80\)[/tex], there are 55 students.
- For marks [tex]\(<100\)[/tex], there are 60 students.
3. Frequency Distribution:
- We need to create a frequency distribution to detail how many students fall within specific ranges of marks.
### Developing Frequency Distribution:
- Range: [tex]\( 0 \leq \text{Marks} < 20 \)[/tex]
- Number of students in this range: 9 (Since it is given that 9 students scored less than 20)
- Range: [tex]\( 20 \leq \text{Marks} < 40 \)[/tex]
- Number of students in this range: [tex]\( 23 - 9 = 14 \)[/tex]
- This is found by subtracting the number of students who scored less than 20 from the total who scored less than 40.
- Range: [tex]\( 40 \leq \text{Marks} < 50 \)[/tex]
- Number of students in this range: [tex]\( 43 - 23 = 20 \)[/tex]
- This is found by subtracting the number of students who scored less than 40 from those who scored less than 50.
- Range: [tex]\( 50 \leq \text{Marks} < 80 \)[/tex]
- Number of students in this range: [tex]\( 55 - 43 = 12 \)[/tex]
- This is found by subtracting the number of students who scored less than 50 from those who scored less than 80.
- Range: [tex]\( 80 \leq \text{Marks} < 100 \)[/tex]
- Number of students in this range: [tex]\( 60 - 55 = 5 \)[/tex]
- This is found by subtracting the number of students who scored less than 80 from those who scored less than 100.
### Concluding Frequency Distribution:
The frequency distribution is as follows:
- Marks 20: 9 students
- Marks 40: 14 students
- Marks 50: 20 students
- Marks 80: 12 students
- Marks 100: 5 students
Thus, the final frequency distribution for the marks and number of students is:
```plaintext
[(20, 9), (40, 14), (50, 20), (80, 12), (100, 5)]
```
This lists the number of students who fall within each specified range of marks.
