Calculate population standard deviation.

1. 3.1 - 1
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20

2. 3.1 - 2
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 


3. 3.1 - 3
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Calculate the mean

4. 3.1 - 4
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Calculate the mean

5. 3.1 - 5
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35

6. 3.1 - 6
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20

7. 3.1 - 7
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35

8. 3.1 - 8
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
10-3535
35
35
35
35
35

9. 3.1 - 9
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25

10. 3.1 - 10
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25

11. 3.1 - 11
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15

12. 3.1 - 12
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5

13. 3.1 - 13
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5

14. 3.1 - 14
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Create a column of each
value minus the mean
µ = 35
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15

15. 3.1 - 15
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15

16. 3.1 - 16
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625

17. 3.1 - 17
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625

18. 3.1 - 18
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225

19. 3.1 - 19
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25

20. 3.1 - 20
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25

21. 3.1 - 21
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Square each deviation
from the mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25
225

22. 3.1 - 22
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Sum the squared
deviations from the
mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25
225

23. 3.1 - 23
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
N
x 

2
)( 

Sum the squared
deviations from the
mean
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25
225
1750

24. 3.1 - 24
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25
225
1750
6
1750
)( 2




N
x 


25. 3.1 - 25
Example 13: Outdoor Paint
An experimental brand of outdoor paint is tested to
see how long it will last before fading (in months). Six
cans of the brand constitutes a small population.
Find the standard deviation.
10, 60, 50, 30, 40, 20
Months, x µ x - µ (x - µ)2
10
60
50
30
40
20
35
35
35
35
35
35
-25
25
15
-5
5
-15
625
625
225
25
25
225
1750
1.17
6
1750
)( 2





N
x 
