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Cumulative Frequency Plot

A cumulative frequency plot is a way to display cumulative information graphically. It shows the number, percentage, or proportion of observations in a data set that are less than or equal to particular values.

In a data set, the cumulative frequency for a value x is the total number of scores that are less than or equal to x. The charts below illustrate the difference between frequency and cumulative frequency. Both charts show scores for a test administered to 300 students.

In the first chart, column height shows frequency - the number of students in each test score grouping. For example, about 30 students received a test score between 51 and 60.

 
Frequency
 
100
80
60
40
20
 
 
 
 
 
 
  41-50 51-60 61-70 71-80 81-90 91-100

In the next chart, column height shows cumulative frequency - the number of students up to and including each test score. This is a cumulative frequency chart. It shows that 30 students received a test score of at least 50; 60 students received a score of at least 60; 120 students received a score of at least 70; and so on.

 
Cumulative
frequency
 
300
240
180
120
60
 
 
 
 
 
 
  50 60 70 80 90 100
See also:   AP Statistics Tutorial: Cumulative Frequency Plots