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 2 cm to 5 books on the horizontal axis and 2 cm to 10 students on the vertical axis, draw an ogive for the data.
Solution:
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)
