UPSC NDA Math Model Paper 9

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 valuesx1+k,x2+k,........,xn+k is σ