What Makes the Standard Deviation Larger or Smaller?
You will find 15 pairs of graphs on the next four pages. The mean for each graph () is given just
above each histogram. For each pair of graphs presented below
1. Indicate whether one of the graphs has a larger standard deviation than the other or if the two
graphs have the same standard deviation.
2. Try to identify the characteristics of the graphs that make the standard deviation larger or smaller.
You can check your answers against the instructor’s answer key as you complete each page.
1.
A
 = 2.57
B
5
4
3
2
1
0
2.
 = 3.33
A has a larger standard
deviation than B
6
FREQUENCY
FREQUENCY
6
A
1 2 3 4
SCORE
5
5
4
3
B has a larger standard
deviation than A
2
1
6
Both graphs have the
same standard deviation
0
 = 2.33
1 2 3 4
SCORE
B
5
6
 = 3.33
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
3.
A
 = .33
B
 = 4.33
6
FREQUENCY
FREQUENCY
6
5
4
3
2
1
0 1 2 3 4
SCORE
5 6
5
4
3
A has a larger standard
deviation than B
B has a larger standard
deviation than A
2
1
Both graphs have the
same standard deviation
0 1 2 3 4
SCORE
5 6
4.
A
 = 2.50
B
 = 2.56
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
5.
A
 = 2.50
B
5
4
3
2
1
0
6.
 =2.50
A has a larger standard
deviation than B
6
FREQUENCY
FREQUENCY
6
A
1 2 3 4
SCORE
5
5
4
3
B has a larger standard
deviation than A
2
1
6
Both graphs have the
same standard deviation
0
 = 2.50
B
1 2 3 4
SCORE
5
6
 = 2.50
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
7.
 = 2.00
B
FREQUENCY
FREQUENCY
A
6
5
4
3
2
1
0
1 2 3 4
SCORE
5
6
 = 2.00
A has a larger standard
deviation than B
6
5
4
3
B has a larger standard
deviation than A
2
1
Both graphs have the
same standard deviation
0
1 2 3 4
SCORE
5
6
8.
 = 1.93
6
5
4
3
2
1
0
9.
B
FREQUENCY
FREQUENCY
A
1 2 3 4
SCORE
5
0
B
FREQUENCY
FREQUENCY
5
4
3
2
1
6
 = 2.00
A has a larger standard
deviation than B
1 2 3 4
SCORE
5
4
3
6
2
1
A
B
0 2 4 6 8 10 12
SCORE
5
6
 = 5.86
A has a larger standard
deviation than B
B has a larger standard
deviation than A
2
1
Both graphs have the
same standard deviation
0 2 4 6 8 10 12
SCORE
B
FREQUENCY
2
1
1 2 3 4
SCORE
6
5
4
3
 = 5.43
6
5
4
3
Both graphs have the
same standard deviation
0
 = 5.43
6
5
4
3
B has a larger standard
deviation than A
2
1
0 2 4 6 8 10 12
SCORE
FREQUENCY
5
5
FREQUENCY
FREQUENCY
A
11.
1 2 3 4
SCORE
6
0
10.
Both graphs have the
same standard deviation
2
1
 = 1.93
A
A has a larger standard
deviation than B
B has a larger standard
deviation than A
6
5
4
3
6
6
 = 2.00
 = 5.57
6
5
4
3
A has a larger standard
deviation than B
B has a larger standard
deviation than A
2
1
Both graphs have the
same standard deviation
0 2 4 6 8 10 12
SCORE
12.
 = 5.33
6
5
4
3
2
1
0 2 4 6 8 10 12
SCORE
13.
A
B
FREQUENCY
FREQUENCY
A
 = 8.33
 = 5.48
6
5
4
3
A has a larger standard
deviation than B
B has a larger standard
deviation than A
2
1
Both graphs have the
same standard deviation
0 2 4 6 8 10 12
SCORE
B
 = 5.00
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
14.
A
 = 6.15
B
 = 3.38
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
15.
A
 = 5.86
B
 = 3.38
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
Answers to the items:
ITEM
sd of Graph A
sd of Graph B
Correct Decision
1
 = 1.365
 = 1.491
B is larger
2
 = .471
 = .943
B is larger
3
 = .471
 = .471
SAME
4
 = 1.708
 = 1.012
A is larger
5
 = 1.708
 = 2.50
B is larger
6
 = 1.803
 = 1.708
A is larger
7
 = 1.00
 = 1.686
B is larger
8
 = 1.280
 = 1.686
B is larger
9
 = 1.280
 = 1.00
A is larger
10
 = 1.400
 = 2.799
B is larger
11
 = 1.400
 = 1.400
SAME
12
 = 1.743
 = 1.332
A is larger
13
 = 1.743
 = 2.415
B is larger
14
 = 2.646
 = 2.075
A is larger
15
 = 3.126
 = 2.075
A is larger