Ogives 6 / 7

Cumulative frequency distributions

Cumulative frequencies are obtained by adding the individual frequencies together.

Ogive

An ogive is a graph of the cumulative number of items with a value less than or equal to, or alternatively greater than or equal to, a certain amount.

It is drawn by plotting a diagram of a cumulative frequency distribution.

Notice:

  • a frequency distribution can be graphed as a histogram

  • a cumulative frequency distribution can be graphed as an ogive.

Illustration

Here, we have a number of students (Frequency) and how many hours they study per week.

See how A Cumulative frequency distribution is calculated:

 Hours Spent to study Number of Students (Frequency) Cumulative Frequency
 <1 10 10
 <3 15 10 + 15 = 25
 <4 4 10 + 15 + 4 = 29
 <6 3 10 + 15 + 4 + 3 = 32
 <10 1 10 + 15 + 4 + 3 + 1 = 33
Diagram

The cumulative frequency distribution shows that, of the total of 33 students:

10 students study less than 1 hour per week, 
25 students study less than 3 hours per week, 
29 students study less than 4 hours per week, 
32 students study less than 6 hours per week and 
33 students study less than 10 hours per week.

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