Question
The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?
NDA
Mathematics
Statistics
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 2.25
- B. 3.5
- C. 4.25
- D. 5.5
Answer
A. 2.25
Step-by-step solution
Let the original observations be x_1, x_2, , x_ 100 . The original arithmetic mean is x = 50. The new observations are given by y_i = x_i - 5 20 . Using the property of arithmetic mean, if each observation is subjected to a linear transformation y_i = a x_i + b, the new mean is y = a x + b. Therefore, the new mean is y = x - 5 20 . Substituting x = 50, we get y = 50 - 5 20 = 45 20 = 2.25. Answer: 2.25
Related: Mathematics — Statistics · All PYQ Banks