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