What Makes the Standard Deviation Larger or Smaller?
You will find 15 pairs of graphs on the next several pages. The mean for each graph (m) 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 item or page.
1. 
A m = 2.57 B m = 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 m = 2.33 B m = 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 m = .33 B m = 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 
4. 
A m = 2.50 B m = 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 m = 2.50 B m =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 
6. 
A m = 2.50 B m = 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. 
A m = 2.00 B m = 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 
8. 
A m = 1.93 B m = 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 
9. 
A m = 1.93 B m = 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 
10. 
A m = 5.43 B m = 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 
11. 
A m = 5.43 B m = 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 
12. 
A m = 5.33 B m = 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 
13. 
A m = 8.33 B m = 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 m = 6.15 B m = 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 m = 5.86 B m = 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 
s = 1.365 
s = 1.491 
B is larger  
2 
s = .471 
s = .943 
B is larger  
3 
s = .471 
s = .471 
SAME  
4 
s = 1.708 
s = 1.012 
A is larger  
5 
s = 1.708 
s = 2.50 
B is larger  
6 
s = 1.803 
s = 1.708 
A is larger  
7 
s = 1.00 
s = 1.686 
B is larger  
8 
s = 1.280 
s = 1.686 
B is larger  
9 
s = 1.280 
s = 1.00 
A is larger  
10 
s = 1.400 
s = 2.799 
B is larger  
11 
s = 1.400 
s = 1.400 
SAME  
12 
s = 1.743 
s = 1.332 
A is larger  
13 
s = 1.743 
s = 2.415 
B is larger  
14 
s = 2.646 
s = 2.075 
A is larger  
15 
s = 3.126 
s = 2.075 
A is larger 