# Cumulative Frequency

Cumulative frequency is defined as a running total of frequencies. The frequency of an element in a set refers to how many of that element there are in the set. Cumulative frequency can also defined as the sum of all previous frequencies up to the current point.

The cumulative frequency is important when analyzing data, where the value of the cumulative frequency indicates the number of elements in the data set that lie below the current value. The cumulative frequency is also useful when representing data using diagrams like histograms.

Cumulative Frequency Table

The cumulative frequency is usually observed by constructing a cumulative frequency table. The cumulative frequency table takes the form as in the example below.

Example 1:

The set of data below shows the ages of participants in a certain summer camp. Draw a cumulative frequency table for the data.

 Age (years) Frequency 10 3 11 18 12 13 13 12 14 7 15 27

Solution:

The cumulative frequency at a certain point is found by adding the frequency at the present point to the cumulative frequency of the previous point.

The cumulative frequency for the first data point is the same as its frequency since there is no cumulative frequency before it.

 Age (years) Frequency Cumulative Frequency 10 3 3 11 18 3+18 = 21 12 13 21+13 = 34 13 12 34+12 = 46 14 7 46+7 = 53 15 27 53+27 = 80

Ogive graph

A cumulative frequency graph, also known as an Ogive, is a curve showing the cumulative frequency for a given set of data. The cumulative frequency is plotted on the y-axis against the data which is on the x-axis for un-grouped data. When dealing with grouped data, the Ogive is formed by plotting the cumulative frequency against the upper boundary of the class. An Ogive is used to study the growth rate of data as it shows the accumulation of frequency and hence its growth rate.