Frequency Diagram

Here we will learn about frequency diagrams, including what they are and how to construct them.

There are also frequency diagram worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a frequency diagram?

A frequency diagram is a way of representing data from a frequency table. 

Frequency diagrams are usually bar charts, vertical line charts or frequency polygons with frequency displayed on the vertical axis.

What is a frequency diagram?

Bar charts

Bar charts represent data using rectangular bars that are the same width. They can be used for categorical data (such as favourite colour, types of food, or makes of car) or numerical data (such as goals scored, height, or time).

Bar charts can also be used for grouped numerical data.

Step-by-step guide: Bar charts

Vertical line charts

Vertical line charts represent data by drawing straight lines to a given frequency.

They can be used for ungrouped numerical data.

Frequency polygons

A frequency polygon is a graph that shows the frequencies of grouped data. It is a type of frequency diagram that plots the midpoints of the class intervals against the frequencies and then joins up the points with straight lines.

Step-by-step guide: Frequency polygon

How to draw a frequency diagram

In order to draw a frequency diagram:

1. Draw a pair of axes and label them.
2. Draw a bar (or vertical line) for each of the items.

How to draw a frequency diagram

Related lessons on representing data

Frequency diagram is part of our series of lessons to support revision on representing data. You may find it helpful to start with the main representing data lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Representing data
• Line graph
• Pie chart
• Scatter graphs
• Two way tables
• Frequency graph
• x and y axis
• Time series graph
• Tally chart
• Stem and leaf diagram
• Pictograph

Frequency diagram examples

Example 1: categorical data – bar chart

Draw a bar chart for this data:

1. Draw a pair of axes and label them.

Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. The categories should be evenly spaced along the horizontal axis.

2Draw a bar (or vertical line) for each of the items.

The heights of the bars need to correspond with their frequencies. The bars should have equal width.

Example 2: categorical data – bar chart

Draw a bar chart for this data:

Draw a pair of axes and label them.

Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. The categories should be evenly spaced along the horizontal axis.

Draw a bar (or vertical line) for each of the items.

The heights of the bars need to correspond with their frequencies. The bars should have equal width.

Example 3: ungrouped numerical data – vertical line chart

Draw a vertical line chart for this data:

Draw a pair of axes and label them.

Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. The categories should be evenly spaced along the horizontal axis.

Draw a bar (or vertical line) for each of the items.

The heights of the vertical lines need to correspond with their frequencies.

Example 4: ungrouped numerical data – vertical line chart

Draw a vertical line chart for this data:

Draw a pair of axes and label them.

Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. The categories should be evenly spaced along the horizontal axis.

Draw a bar (or vertical line) for each of the items.

The heights of the vertical lines need to correspond with their frequencies.

Example 5: grouped numerical data – bar chart

Draw a bar chart for this grouped data:

Draw a pair of axes and label them.

Look at Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. Use the ends of the class intervals to help put the numbers on the horizontal axis – 0, 100, 200 and so on.

Draw a bar (or vertical line) for each of the items.

The heights of the bars need to correspond with their frequencies. The bars should have equal width.

Example 6: grouped numerical data – bar chart

Draw a bar chart for this grouped data:

Draw a pair of axes and label them.

Look at what the highest frequency is. The vertical axis for the frequency needs to go up at least as high as this frequency. Use the ends of the class intervals to help put the numbers on the horizontal axis – 0, 10, 20 and so on.

Draw a bar (or vertical line) for each of the items.

The heights of the bars need to correspond with their frequencies.

Common misconceptions

• Equal widths

The bars for frequency diagrams should all have the same width. The vertical lines should also have the same thickness.

• Frequencies are whole numbers

Since frequencies are a count of how many times an item occurs, they will always be integers.  They are not decimals.

• Gaps between bars

For categorical data, there should be a gap between each bar on a bar chart. This allows the data to be easier to interpret.

The next lessons are

• Mean, median, mode
• Frequency table
• Cumulative frequency

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