Question
The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?
NDA
Mathematics
Statistics
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 0.25
- B. 0.5
- C. 0.75
- D. 1.00
Answer
B. 0.5
Step-by-step solution
Let the original observations be x_1, x_2, , x_ 100 . The standard deviation of these observations is _x = 10. The new observations are given by y_i = x_i + 5 20 = 1 20 x_i + 1 4 . If a new variable is defined as y_i = ax_i + b, its standard deviation is given by _y = |a| _x. Substituting a = 1 20 and _x = 10: _y = | 1 20 | 10 = 0.5 The new standard deviation is 0.5. Answer: 0.5
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