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Cumulative Grouped Frequency Tables (Mathematics Glossary)

What Is a Cumulative Grouped Frequency Table?

A cumulative grouped frequency table is a grouped frequency table with a running total of the frequencies.

Imagine you had a set of numbers:



A cumulative grouped frequency table is a way to present this data in a simpler way:

Understanding the Cumulative Grouped Frequency Table

A cumulative grouped frequency table is a grouped frequency table with a Cumulative frequency column.

Let's look again at our list of numbers (rearranged in order and each group of numbers counted):

  • The Group column of the grouped frequency table contains the groups into which we group the numbers in the list.

  • The Frequency column of the grouped frequency table contains how often a number from within each group appears in this list.
This gives us a grouped frequency table:



  • The Cumulative frequency column keeps a running total on the frequency.

    • The cumulative frequency in the first row is equal to the frequency:


    • The cumulative frequency in the second row is found by adding the frequency in this row to all the frequencies above:



      Note: It is also found by adding the frequency in this row to the cumulative frequency above.

    • The cumulative frequency in the third row is found by adding the frequency in this row to all the frequencies above:



      Note: It is also found by adding the frequency in this row to the cumulative frequency above.

    • The cumulative grouped frequency table is complete when all the cumulative frequencies have been entered:

How to Make a Cumulative Grouped Frequency Table

Making a cumulative grouped frequency table is easy.

The first step is to make a grouped frequency table. Then complete the Cumulative frequency column by adding the frequencies.



Read more about how to make a cumulative grouped frequency table

Other Types of Frequency Table

  • A grouped frequency table is a grouped frequency table that has another column which keeps a running total of the frequencies.


  • A frequency table shows how often (how frequently) each number appears in a list of numbers.


  • A cumulative frequency table is a frequency table that has another column which keeps a running total of the frequencies.

Read more about grouped frequency tables
Read more about frequency tables
Read more about cumulative frequency tables

Interactive Test
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Here's a second test on grouped frequency tables.
Here's a third test on grouped frequency tables.
Top Tip

Cumulative Grouped Frequency Tables Are for Continuous Data

A cumulative grouped frequency table is for continuous data.

Continuous data can take any value (within a range). For example, it may take any value from 1 - 10: 1.5, 2.31, 3.05.

This is unlike discrete data, which can only take certain values. For example: 1, 2, 3. It can't take values in between these values: it can't take 1.5.

Quick Check

The final entry in the Cumulative frequency column must equal the total of the Frequency column.

Add up the Frequency column to see if it is the same as the last number you write in the Cumulative frequency column:

The Cumulative Frequency Is Increasing

The numbers in the Cumulative frequency column must increase as you go down the rows.



This is because each time you go down a row, you add another frequency to the running total, so it must get larger.

Sometimes a the cumulative frequency will stay the same. What must the frequency be in that row?

Note

What's in a Name?

"Cumulative" means increasing by one addition after another.

"Frequency" means how often something occurs.

Other Column Headings

In the frequency table, the column headings are Group, Frequency and Cumulative frequency.

This needn't be the case.

Each group is a grouping of numbers. The numbers could represent many things: test scores, incomes, heights, number of pets. Use a descriptive heading in the frequency table (Score, Income, Height, No. of pets).