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Frequency Tables (Mathematics Glossary)

What Is a Frequency Table?

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

Imagine you had a set of numbers:



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

Understanding the Frequency Table

The frequency table tells you each number that appears in a list of numbers and how many times each number appears.

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

  • We see that 5 appears 2 times.

    We write 5 in the Number column. It is the lowest number that appears in the list of numbers.

    We write 2 in the Frequency column because 5 appears 2 times in the list of numbers.


  • We see that 6 appears 3 times.

    We write 6 in the Number column. It is the next number (in numeric order) that appears in the list of numbers.

    We write 3 in the Frequency column because 6 appears 3 times in the list of numbers.

The frequency table is complete when all numbers and their frequencies have been entered:

How to Make a Frequency Table

Making a frequency table is easy.

It just requires being able to count how often each number appears in a list of numbers and transferring that to a table. Using a tally system is a good way to check you are counting the numbers off correctly:



Read more about how to make a frequency table

Finding Averages from a Frequency Table

The frequency table can be used to find the average of a set of numbers.

A frequency table can be used to find: Read more about how to find the mean from a frequency table.
Read more about how to find the median from a frequency table.
Read more about how to find the mode from a frequency table.

Other Types of Frequency Table

The frequency tables shown on this page are the basic type of frequency table. There are further variations on the basic frequency table. Read more about cumulative 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 frequency tables.
Here's a third test on frequency tables.
Top Tip

Frequency Tables Are for Discrete Data

A 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.

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 he pets that students have:
Dog, Cat, Rabbit, Dog, Dog, Cat, Fish
This could be presented in a frequency table: