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Cumulative Frequency Tables (Mathematics Glossary)

What Is a Cumulative Frequency Table?

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

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

Imagine you had a set of numbers:



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

Understanding the Cumulative Frequency Table

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

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

  • The Number column of the frequency table contains each number in this list.

  • The Frequency column of the frequency table contains how often each number appears in this list.
This gives us a 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 frequency table is complete when all the cumulative frequencies have been entered:

How to Make a Cumulative Frequency Table

Making a cumulative frequency table is easy.

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



Read more about how to make a cumulative frequency table

Other Types of Frequency Table

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


  • A grouped frequency table groups numbers together. It shows you how often numbers within each group appear in a list of numbers.


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

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

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

Cumulative Frequency Tables Are for Discrete Data

A cumulative frequency table is for discrete data.

Discrete data 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.

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

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 cumulative frequency table, the column headings are Number, Frequency and Cumulative frequency.

This needn't be the case.

Imagine the numbers in the list represented test scores. A more descriptive heading for the Number column might be Score.

The numbers could represent many other things: incomes, heights, number of pets. Use a descriptive heading in the frequency table (Income, Height, No. of pets).

Cumulative Frequency Tables with Non-Numeric Items

The items in a set needn't be numbers.

Imagine there was a list of he pets that students have:
Dog, Cat, Rabbit, Dog, Dog, Cat, Fish
This could be presented in a cumulative frequency table: