Correct Answer - Option 1 : σ
Concept:
if each observation is increased by a constant k, then the standard deviation is unchanged.
Calculations:
Given, A set of n values x1, x2,..., xn has standard deviation σ.
Consider, the data x1 + k, x2 + k,..., xn + k
Here, each observation is increased by a constant k,
we know that, if each observation is increased by a constant k, then the standard deviation is unchanged.
Hence, the standard deviation of n values x1 + k, x2 + k,..., xn + k is σ