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: Problem Definition: Given a cumulative frequency distribution of student marks and counts, determine the modal class, which represents the class interval with the highest student frequency.

Step 2: Frequency Calculation:
The provided cumulative frequencies are:
- Below 10: 3
- Below 20: 12
- Below 30: 27
- Below 40: 57
- Below 50: 75

Individual class frequencies are derived by subtracting consecutive cumulative frequencies:
- 0-10: 3
- 10-20: \( 12 - 3 = 9 \)
- 20-30: \( 27 - 12 = 15 \)
- 30-40: \( 57 - 27 = 30 \)
- 40-50: \( 75 - 57 = 18 \)

The resulting 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: Modal Class Identification:
The class interval with the highest frequency is 30-40, with 30 students.

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