What happens to the median, mode, and standard deviation when 3 is added to every value in a data set?

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.