*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:

## 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.

## 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?

"Frequency" means how often something occurs.## Other Column Headings

In the frequency table, the column headings are**Number**and

**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**).

## Frequency Tables with Non-Numeric Items

The items in a set needn't be numbers. Imagine there was a list of the pets that students have:
Dog, Cat, Rabbit, Dog, Dog, Cat, Fish

This could be presented in a cumulative frequency table:## You might also like...

statisticsfinding the range from a frequency tablemaking a cumulative frequency tableunderstanding grouped frequency tables

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