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.
