Math 123- Statistics
Comparing Standard Deviations Activity
There are 8 pairs of graphs where the population mean for each graph is given. For each pair of
graphs, determine which graph has the larger standard deviation. Note: In some cases, the
standard deviations of the two graphs are equal. Try to identify the characteristics of the graphs that
make the standard deviation larger or smaller.
1.
A
 = 2.33
B
 = 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
2.
A
 = .33
B
 = 4.33
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
 = 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
4.
A
 = 2.50
B
 =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
5.
A
 = 1.93
B
 = 2.00
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
6.
A
 = 5.43
B
 = 5.86
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
7.
A
 = 5.43
B
 = 5.57
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
8.
A
 = 5.33
B
 = 5.48
A has a larger standard
deviation than B
B has a larger standard
deviation than A
Both graphs have the
same standard deviation
Answers
1. B has larger standard deviation than A.
Reason: B has more spread, so B has a larger standard deviation.
2. Both graphs have the same standard deviation.
Reason: Both graphs are the same, just shifted, so the standard deviation doesn’t change.
3. A has larger standard deviation than B.
Reason: A has more spread, so A has a larger standard deviation.
4. B has larger standard deviation than A.
Reason: B has bars that are further from the population mean, so B has a larger standard deviation.
5. B has larger standard deviation than A.
Reason: B has tall bars that are far out from the mean, so B has a larger standard deviation.
6. B has larger standard deviation than A.
Reason: The graphs are the same except that B is more spread out, so B has a larger standard
deviation.
7. Both graphs have the same standard deviation.
Reason: Both graphs are the same, just reflected, so the standard deviation doesn’t change.
8. A has larger standard deviation than B.
Reason: A has tall bars everywhere along the graph, so A has a larger standard deviation.
Flash Cards for groups located on the
following 3 pages
1.
A
 = 2.33
B
 = 3.33
2.
A
 = .33
B
 = 4.33
3.
A
B
 = 2.56
4.
A
B
 =2.50
 = 2.50
 = 2.50
B
 = 2.00
 = 5.43
B
 = 5.86
A
 = 5.43
B
 = 5.57
A
 = 5.33
B
 = 5.48
5.
A
6.
A
7.
8.
 = 1.93
A has a larger
standard deviation
than B.
B has a larger
standard deviation
than A.
Both graphs have
the same standard
deviation.