Sure! Let's walk through the process of creating a frequency distribution table based on the given data.
1. Understanding the Table:
- We have the number of students with marks in certain ranges.
- "Marks" refers to the interval ranges.
- "No. of students" refers to the cumulative number of students scoring more than or equal to a certain mark.
2. Intervals:
- These intervals can be denoted as: [0-10), [10-20), [20-30), [30-40), [40-50).
3. Cumulative Frequencies:
- These are the cumulative numbers of students who have scored more than or equal to the lower boundary of each interval.
4. Frequency Calculation:
- Calculate the number of students in each interval by subtracting successive cumulative frequencies.
Given data for cumulative frequencies:
- 0 mark --> 63 students
- 10 marks --> 58 students
- 20 marks --> 55 students
- 30 marks --> 51 students
- 40 marks --> 48 students
- 50 marks --> 42 students.
Step-by-step calculation:
- Students scoring in the interval [0-10):
[tex]\(63 - 58 = 5\)[/tex]
- Students scoring in the interval [10-20):
[tex]\(58 - 55 = 3\)[/tex]
- Students scoring in the interval [20-30):
[tex]\(55 - 51 = 4\)[/tex]
- Students scoring in the interval [30-40):
[tex]\(51 - 48 = 3\)[/tex]
- Students scoring in the interval [40-50):
[tex]\(48 - 42 = 6\)[/tex]
5. Frequency Distribution Table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Interval (Marks)} & \text{Frequency (No. of students)} \\
\hline
0-10 & 5 \\
10-20 & 3 \\
20-30 & 4 \\
30-40 & 3 \\
40-50 & 6 \\
\hline
\end{array}
\][/tex]
So, the completed frequency distribution table indicates the number of students scoring within each range of marks:
- 5 students scored between 0 and 10.
- 3 students scored between 10 and 20.
- 4 students scored between 20 and 30.
- 3 students scored between 30 and 40.
- 6 students scored between 40 and 50.
