 # 7.1.4 Cumulative Frequency

7.1.4 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:
(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) 