Question
The frequency distribution of the marks obtained by students in a Science examination is given below: Marks 5–15 15–25 25–35 35–45 Number of students 20 30 30 20 What is the arithmetic mean?
NDA
Mathematics
Statistics
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 20
- B. 25
- C. 30
- D. 35
Answer
B. 25
Step-by-step solution
The class marks (midpoints) x_i for the given intervals are 10, 20, 30, 40. The corresponding frequencies f_i are 20, 30, 30, 20. Total number of students, N = f_i = 20 + 30 + 30 + 20 = 100 Calculating the sum of f_i x_i: f_i x_i = (20 10) + (30 20) + (30 30) + (20 40) f_i x_i = 200 + 600 + 900 + 800 = 2500 Arithmetic mean x = f_i x_i N = 2500 100 = 25 Answer: 25
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