UPSC NDA I 2025 Mathematics Paper

Given,
Number of observations, n=100
Original standard deviation, σ=10
Transformation applied to each observation:
New value, x′=‌

x+5

20

The additive constant (5) does not affect the standard deviation, and scaling by 20 divides the standard deviation by 20 , so the new standard deviation is,
σ′‌=‌

σ

20

σ′‌=‌

10

20

=0.5
∴ The new standard deviation is 0.5.