Sample Standard Deviation

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

3.1 - 2
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
1
)( 2




n
xx
s

3.1 - 3
1
)( 2




n
xx
s
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Calculate the mean

3.1 - 4
1
)( 2




n
xx
s
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Calculate the mean

3.1 - 5
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
Create a column of each
value minus the mean
1
)( 2




n
xx
s

3.1 - 6
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
1
)( 2




n
xx
s

3.1 - 7
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
)( 2




n
xx
s

3.1 - 8
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
11.2-12.612.6
12.6
12.6
12.6
12.6
12.6
1
)( 2




n
xx
s

3.1 - 9
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 1
)( 2




n
xx
s

3.1 - 10
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
1
)( 2




n
xx
s

3.1 - 11
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
1
)( 2




n
xx
s

3.1 - 12
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
1
)( 2




n
xx
s

3.1 - 13
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
)( 2




n
xx
s

3.1 - 14
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
)( 2




n
xx
s

3.1 - 15
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
)( 2




n
xx
s

3.1 - 16
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 17
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 18
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 19
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 20
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 21
11.2, 11.9, 12.0, 12.8, 13.4, 14.3
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
)( 2




n
xx
s

3.1 - 22
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
)( 2




n
xx
s

3.1 - 23
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
)( 2




n
xx
s

3.1 - 24
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
1
)( 2





n
xx
s

3.1 - 25
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
)( 2






n
xx
s

Sample Standard Deviation

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