6.5 Cumulative Frequency

6.5 Cumulative Frequency
Cumulative Frequency of a data or a class interval in a frequency table is obtained by determining the sum of its frequency with the total frequencies of all its previous data or class interval.
 
(A) Ogive
Ogive is a cumulative frequency graph which is obtained by plotting the cumulative frequency against the upper boundaries of each class.
 
Example:
The data below shows the number of books read by a group of 60 students in a year.
 
Books
Frequency
6-10
3
11-15
7
16-20
11
21-25
16
26-30
11
31-35
8
36-40
4
(a) Construct a cumulative frequency table for the given data.
(b) By using the scales of 2cm to 5 books on the horizontal axis and 2cm 
  to 10 students on the vertical axis, draw an ogive for the data. 

Solution:
(a)
  • Add a class with frequency 0 before the first class.
  • Find the upper boundary of each class interval.

Books
Frequency
Cumulative Frequency
Upper Boundary
1-5
0
0
5.5
6-10
3
0 + 3 = 3
10.5
11-15
7
3 + 7 = 10
15.5
16-20
11
10 + 11 = 21
20.5
21-25
16
21 + 16 = 37
25.5
26-30
11
37 + 11 = 48
30.5
31-35
8
48 + 8 = 56
35.5
36-40
4
56 + 4 = 60
40.5
(b)


 

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