# 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.

- 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:

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

# 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 grouped frequency tables

Read more about cumulative grouped frequency tables

##### Interactive Test

**show**

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: