The document provides a frequency distribution of the number of miles run per week by individuals. It lists the class boundaries, frequencies, and calculates the midpoints of each class. To find the mean, it multiplies each frequency by its corresponding midpoint, sums the results, and divides by the total frequency.

1. 3.1 - 1
Example 9: Miles Run
Class
Boundaries
Frequency
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
Below is a frequency distribution of the number of miles
run per week for a sample of individuals. Find the mean.

2. 3.1 - 2
Example 9: Miles Run
Class
Boundaries
Frequency
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
Below is a frequency distribution of the number of miles
run per week for a sample of individuals. Find the mean.
( )f x
x
f
 



3. 3.1 - 3
Example 9: Miles Run
Class
Boundaries
Frequency
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
Below is a frequency distribution of the number of miles
run per week for a sample of individuals. Find the mean.
( )f x
x
f
 


Sum the frequencies

4. 3.1 - 4
Example 9: Miles Run
Class
Boundaries
Frequency
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
Below is a frequency distribution of the number of miles
run per week for a sample of individuals. Find the mean.
f = 20
( )f x
x
f
 


Sum the frequencies

5. 3.1 - 5
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
f = 20

 

f
xf
X
)( Midpoint

6. 3.1 - 6
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
f = 20

 

f
xf
X
)(

7. 3.1 - 7
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
f = 20

 

f
xf
X
)(

8. 3.1 - 8
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
f = 20

 

f
xf
X
)(

9. 3.1 - 9
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
f = 20

 

f
xf
X
)(

10. 3.1 - 10
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
f = 20

 

f
xf
X
)(

11. 3.1 - 11
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
f = 20

 

f
xf
X
)(

12. 3.1 - 12
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20

 

f
xf
X
)(

13. 3.1 - 13
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
f ·x

 

f
xf
X
)( Multiply each
frequency by the
class midpoint

14. 3.1 - 14
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
f ·x

 

f
xf
X
)(

15. 3.1 - 15
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
f ·x

 

f
xf
X
)(

16. 3.1 - 16
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
f ·x

 

f
xf
X
)(

17. 3.1 - 17
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
f ·x

 

f
xf
X
)(

18. 3.1 - 18
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
f ·x

 

f
xf
X
)(

19. 3.1 - 19
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
f ·x

 

f
xf
X
)(

20. 3.1 - 20
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
2×38 = 76
f ·x

 

f
xf
X
)(

21. 3.1 - 21
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
2×38 = 76
f ·x

 

f
xf
X
)(
Sum the products

22. 3.1 - 22
Example 9 Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
2×38 = 76
f ·x
 (f ·x) = 490

 

f
xf
X
)(

23. 3.1 - 23
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
2×38 = 76
f ·x
 (f ·x) = 490
20
490)(





f
xf
X

24. 3.1 - 24
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.5
10.5 - 15.5
15.5 - 20.5
20.5 - 25.5
25.5 - 30.5
30.5 - 35.5
35.5 - 40.5
1
2
3
5
4
3
2
( 5.5 +10.5)/2 = 8
(10.5+15.5)/2 = 13
(15.5+20.5)/2 = 18
(20.5+25.5)/2 = 23
(25.5+30.5)/2 = 28
(30.5+35.5)/2 = 33
(35.5+40.5)/2 = 38
f = 20
1×8 = 8
2×12 = 26
3×18 = 54
5×23 = 115
4×28 = 112
3×33 = 99
2×38 = 76
f ·x
 (f ·x) = 490
5.24
20
490)(





f
xf
X miles