Step by step to calculating the mean of a frequency distribution

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