3.1 - 1

Example 14: Auto SalesFind 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

Example 14: Auto SalesFind 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

1

)( 2

n

xxs

3.1 - 3

1

)( 2

n

xxs

Example 14: Auto SalesFind 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

3.1 - 4

Example 14: Auto Sales

1

)( 2

n

xxs

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

3.1 - 5

Example 14: Auto SalesFind 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

)( 2

n

xxs

3.1 - 6

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

1

)( 2

n

xxs

3.1 - 7

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

1

)( 2

n

xxs

3.1 - 8

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

11.2-12.612.612.612.612.612.612.6

1

)( 2

n

xxs

3.1 - 9

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4 1

)( 2

n

xxs

3.1 - 10

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7

1

)( 2

n

xxs

3.1 - 11

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.6

1

)( 2

n

xxs

3.1 - 12

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.2

1

)( 2

n

xxs

3.1 - 13

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.8

1

)( 2

n

xxs

3.1 - 14

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1

)( 2

n

xxs

3.1 - 15

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1

)( 2

n

xxs

3.1 - 16

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.96 1

)( 2

n

xxs

3.1 - 17

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.49

1

)( 2

n

xxs

3.1 - 18

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.36

1

)( 2

n

xxs

3.1 - 19

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.04

1

)( 2

n

xxs

3.1 - 20

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.64

1

)( 2

n

xxs

3.1 - 21

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.642.89

1

)( 2

n

xxs

3.1 - 22

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.642.89

1

)( 2

n

xxs

3.1 - 23

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.642.896.38

1

)( 2

n

xxs

3.1 - 24

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.642.896.38

5

38.6

1

)( 2

n

xxs

3.1 - 25

Example 14: Auto SalesFind 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

11.211.912.012.813.414.3

12.612.612.612.612.612.6

-1.4-0.7-0.60.20.81.7

1.960.490.360.040.642.896.38 13.1

5

38.6

1

)( 2

n

xxs