Question

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set.

(a) Consider the following data set. 8, 13, 14, 9, 9, and compute s.

(b) Add 4 to each data value to get the new data set 12, 17, 18, 13, 13. Compute s.

Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

a. Adding the same constant c to each data value results in the standard deviation remaining the
same.

b.	Adding the same constant c to each data value results in the standard deviation increasing by c units.

c.	Adding the same constant c to each data value results in the standard deviation decreasing by c units.

d.	There is no distinct pattern when the same constant is added to each data value in a set.

Answer 1

Standard Deviation of sample S =

	Values
	8	6.76 (8 - 10.6)2
	13	5.76 (13 - 10.6)2
	14	11.56 (14 - 10.6)2
	9	2.56 (9 - 10.6)2
	9	2.56 (9 - 10.6)2
Total	53	29.2

Mean = 53 / 5 = 10.6

Standard Deviation S =

S = 29.2 / (5-1)

S = 29.2 / 4

S = 2.7019

Part b)  Add 4 to each data value

	Values
	12	6.76 (12 - 14.6)2
	17	5.76  (17 - 14.6)2​
	18	11.56 (18 - 14.6)2​
	13	2.56 (13 - 14.6)2​
	13	2.56 (13 - 14.6)2​
Total	73	29.2

Mean = 73 / 5 = 14.6

Standard Deviation S =

S = 29.2 / (5-1)

S = 29.2 / 4

S = 2.7019

There is no difference in the standard deviation after adding the constant.

Option a). is correct.