The document calculates the variance and standard deviation of European auto sales over 6 years. It provides the annual sales data in millions of dollars. It walks through the steps of finding the mean, calculating the deviations from the mean, squaring the deviations, and summing the squared deviations to calculate the variance. The goal is to determine the variance and standard deviation for the 6 years of auto sales data provided.

1. 3.1 - 1
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3

2. 3.1 - 2
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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3. 3.1 - 3
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Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Calculate the mean

4. 3.1 - 4
Example 14: Auto Sales
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Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Calculate the mean

5. 3.1 - 5
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
1
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6. 3.1 - 6
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
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7. 3.1 - 7
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
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8. 3.1 - 8
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
11.2-12.612.6
12.6
12.6
12.6
12.6
12.6
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9. 3.1 - 9
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4 1
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s

10. 3.1 - 10
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
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n
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s

11. 3.1 - 11
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
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n
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s

12. 3.1 - 12
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
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13. 3.1 - 13
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
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14. 3.1 - 14
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1
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n
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s

15. 3.1 - 15
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1
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n
xx
s

16. 3.1 - 16
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96 1
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n
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s

17. 3.1 - 17
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
1
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n
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s

18. 3.1 - 18
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
1
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n
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s

19. 3.1 - 19
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
1
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n
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s

20. 3.1 - 20
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
1
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n
xx
s

21. 3.1 - 21
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Square each deviation
from the mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
2.89
1
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n
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s

22. 3.1 - 22
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Sum the squared
deviations from the
mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
2.89
1
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n
xx
s

23. 3.1 - 23
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Sum the squared
deviations from the
mean
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
2.89
6.38
1
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n
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s

24. 3.1 - 24
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
2.89
6.38
5
38.6
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n
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s

25. 3.1 - 25
Example 14: Auto Sales
Find the variance and standard deviation for the
amount of European auto sales for a sample of 6
years. The data are in millions of dollars.
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
x
11.2
11.9
12.0
12.8
13.4
14.3
12.6
12.6
12.6
12.6
12.6
12.6
-1.4
-0.7
-0.6
0.2
0.8
1.7
1.96
0.49
0.36
0.04
0.64
2.89
6.38 13.1
5
38.6
1
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