Question

Marks :	Below 10	Below 20	Below 30	Below 40	Below 50
Number of Students :	3	12	27	57	75

For the above distribution, the modal class is :

• A. 45585
• B. 20-30
• C. 30-40
• D. 40-50

Answer 1

The Correct Option is C

Step 1: Understand the problem:
We are given a cumulative frequency distribution of marks and the number of students. We need to find the modal class. The modal class is the class interval with the highest frequency (i.e., the most students fall into that class).

Step 2: Calculate the frequencies for each class interval:
The cumulative frequencies are given as follows:
- Below 10: 3 students
- Below 20: 12 students
- Below 30: 27 students
- Below 40: 57 students
- Below 50: 75 students
The frequency for each class interval is the difference between two consecutive cumulative frequencies:
- Frequency for 0-10: \( 3 \) (since it’s the first class, it is just 3)
- Frequency for 10-20: \( 12 - 3 = 9 \)
- Frequency for 20-30: \( 27 - 12 = 15 \)
- Frequency for 30-40: \( 57 - 27 = 30 \)
- Frequency for 40-50: \( 75 - 57 = 18 \)
So the frequency distribution is:
- 0-10: 3 students
- 10-20: 9 students
- 20-30: 15 students
- 30-40: 30 students
- 40-50: 18 students

Step 3: Identify the modal class:
The modal class is the class with the highest frequency. From the frequency distribution, we can see that the class interval 30-40 has the highest frequency of 30 students.

Conclusion:
The modal class is \( \boxed{30-40} \).