Adding a constant to each value in a data set does not change the distance between values so the standard deviation remains the same. For example, consider the following numbers 2 , 3 , 4 , 4 , 5 , 6 , 8 , 10 for this set of data the standard deviation would be s = √ ∑ n i=1 ( x i − ¯ x ) 2 n − 1 s = √ ( 2 − 5.25 ) 2 + ( 3 − 5.25 ) 2 + ... + ( 10 − 5.25 ) 2 8 − 1 s = 2.65922 If we were to add 5 to each value in this data set, the new set of values would be: 7 , 8 , 9 , 9 , 10 , 11 , 13 , 15 s = √ ( 7 − 10.25 ) 2 + ( 8 − 10.25 ) 2 + ... + ( 15 − 10.25 ) 2 8 − 1 s = 2.65922 As you can see the s.d. remains the same unless you multiply every value by a constant.