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. Consider the following data set.

12, 6, 11, 10, 15

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)


(b) Add 3 to each data value to get the new data set 15, 9, 14, 13, 18. Compute s. (Enter your answer to one decimal place.)

(c) 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?

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

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

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

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

Answer 1

a)

S.No		X	(X-x̄)	(X-x̄)2
1		12	1.200	1.44000
2		6	-4.800	23.04000
3		11	0.200	0.04000
4		10	-0.800	0.64000
5		15	4.200	17.64000
Σx		54	Σ(X-x̄)2=	42.8000
x̄=Σx/n		10.8000	s2=Σ(x-x̄)2/(n-1)=	10.70000
			s=√s2    =	3.271

s =3.3

b)

S.No		X	(X-x̄)	(X-x̄)2
1		15	1.200	1.44000
2		9	-4.800	23.04000
3		14	0.200	0.04000
4		13	-0.800	0.64000
5		18	4.200	17.64000
Σx		69	Σ(X-x̄)2=	42.8000
x̄=Σx/n		13.8000	s2=Σ(x-x̄)2/(n-1)=	10.70000
			s=√s2    =	3.271

s =3.3

c)

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