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

610

3

1115

7

1620

11

2125

16

2630

11

3135

8

3640

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:
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

15

0

0

5.5

610

3

0 + 3 = 3

10.5

1115

7

3 + 7 = 10

15.5

1620

11

10 + 11 = 21

20.5

2125

16

21 + 16 = 37

25.5

2630

11

37 + 11 = 48

30.5

3135

8

48 + 8 = 56

35.5

3640

4

56 + 4 = 60

40.5
