Question
Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0-10 10-20 20-30 30-40 No. of students 10 20 f 40 Question: What is the standard deviation ?
NDA
Mathematics
Statistics
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 8 5
- B. 9
- C. 9 5
- D. 10
Answer
D. 10
Step-by-step solution
The total number of students is 100. 10 + 20 + f + 40 = 100 f = 30 The mid-points of the class intervals are x_i = 5, 15, 25, 35. The mean x is given by: x = f_i x_i f_i = 10(5) + 20(15) + 30(25) + 40(35) 100 x = 50 + 300 + 750 + 1400 100 = 2500 100 = 25 The variance ^2 is given by: ^2 = f_i (x_i - x )^2 f_i ^2 = 10(5 - 25)^2 + 20(15 - 25)^2 + 30(25 - 25)^2 + 40(35 - 25)^2 100 ^2 = 10(-20)^2 + 20(-10)^2 + 30(0)^2 + 40(10)^2 100 ^2 = 10(400) + 20(100) + 0 + 40(100) 100 ^2 = 4000 + 2000 + 0 + 4000 100 = 10000 100 = 100 The standard deviation is = 100 = 10. Answer: 10
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