GCSE Maths Statistics

Representing Data

Frequency Diagram

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?

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).

Frequency Diagram Image 1

Bar charts can also be used for grouped numerical data.

Frequency Diagram Image 2

Step-by-step guide: Bar charts (coming soon)

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.

Frequency Diagram Image 4

Step-by-step guide: Frequency polygons (coming soon)

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

How to draw a frequency diagram

Frequency polygon worksheet (includes frequency diagram)

Frequency polygon worksheet (includes frequency diagram)

Frequency polygon worksheet (includes frequency diagram)

Get your free frequency diagram worksheet of 20+ frequency polygon questions and answers. Includes reasoning and applied questions.

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Frequency polygon worksheet (includes frequency diagram)

Frequency polygon worksheet (includes frequency diagram)

Frequency polygon worksheet (includes frequency diagram)

Get your free frequency diagram worksheet of 20+ frequency polygon questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Frequency diagram examples

Example 1: categorical data – bar chart

Draw a bar chart for this data:

Frequency Diagram Example 1

  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.

Frequency Diagram Example 1 Step 1

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.

Frequency Diagram Example 1 Step 2

Example 2: categorical data – bar chart

Draw a bar chart for this data:

Frequency Diagram Example 2

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.


Frequency Diagram Example 2 Step 1

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


Frequency Diagram Example 2 Step 2

Example 3: ungrouped numerical data – vertical line chart

Draw a vertical line chart for this data:

Frequency Diagram Example 3.1

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.


frequency diagrams new image 3

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:

Frequency Diagram Example 4

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.


Frequency Diagram Example 4 Step 1

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:

Frequency Diagram Example 5

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.


Frequency Diagram Example 5 Step 1

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


Frequency Diagram Example 5 Step 2

Example 6: grouped numerical data – bar chart

Draw a bar chart for this grouped data:

Frequency Diagram Example 6

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.


Frequency Diagram Example 6 Step 1

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


Frequency Diagram Example 6 Step 2

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.

Practice frequency diagram questions

1. Choose the correct frequency table for the following frequency diagram:

 

Frequency Diagram Practice Question 1

Frequency Diagram Practice Question 1 Answer 1

GCSE Quiz True

Frequency Diagram Practice Question 1 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 1 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 1 Answer 4

GCSE Quiz False

The frequency for Blonde is 4, the frequency for Brown is 5, the frequency for Black is 3 and the frequency for Red is 1.

2. Choose the correct frequency table for the following frequency diagram:

 

Frequency Diagram Practice Question 2

Frequency Diagram Practice Question 2 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 2 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 2 Answer 1

GCSE Quiz True

Frequency Diagram Practice Question 2 Answer 4

GCSE Quiz False

The frequency for Sheep is 5 , the frequency for Cow is 3 , the frequency for Pig is 1 and the frequency for Chicken is 6 .

3. Choose the correct frequency table for the following frequency diagram:

 

Frequency Diagram Practice Question 3

Frequency Diagram Practice Question 3 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 3 Answer 1

GCSE Quiz True

Frequency Diagram Practice Question 3 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 3 Answer 4

GCSE Quiz False

The frequency for 0 siblings is 7 , the frequency for 1 sibling is 5 and the frequency for 2 siblings is 2 .

4. Choose the correct frequency table for the following frequency diagram:

 

Frequency Diagram Practice Question 4

Frequency Diagram Practice Question 4 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 4 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 4 Answer 1

GCSE Quiz True

Frequency Diagram Practice Question 4 Answer 4

GCSE Quiz False

The frequency for 3 apples is 7 , the frequency for 4 apples is 9 , the frequency for 5 apples is 6 , the frequency for 6 apples and the frequency for 7 apples is 1 .

5. Choose the correct grouped frequency table for the following grouped frequency diagram:

 

Frequency Diagram Practice Question 5

Frequency Diagram Practice Question 5 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 5 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 5 Answer 4

GCSE Quiz False

Frequency Diagram Practice Question 5 Answer 1

GCSE Quiz True

The frequency is 2 for values in the range 0-100cm , the frequency is 4 for values in the range of 100-200cm, the frequency is 7 for values in the range of 200-300cm and the frequency is 3 for values in the range of 300-400cm.

6. Choose the correct grouped frequency table for the following grouped frequency diagram:

 

Frequency Diagram Practice Question 6

Frequency Diagram Practice Question 6 Answer 2

GCSE Quiz False

Frequency Diagram Practice Question 6 Answer 1

GCSE Quiz True

Frequency Diagram Practice Question 6 Answer 3

GCSE Quiz False

Frequency Diagram Practice Question 6 Answer 4

GCSE Quiz False

The frequency for 0-10 \; kmph is 5 , the frequency for 10-20 \; kmph is 8 , the frequency for 20-30 \; kmph is 4 and the frequency for 30-40 \; kmph is 1.

Frequency diagram GCSE questions

1. Will recorded the different types of birds visiting his garden.

The table shows his results.

 

Frequency Diagram GCSE Question 1

 

(a) Complete the bar chart to show Will’s results.

 

Frequency Diagram GCSE Question 1a Image 1

 

(b) How many more sparrows than robins were there?

 

(3 marks)

Show answer

(a)

 

Frequency Diagram GCSE Question 1a Image 2

(2)

 

(b)

 

12

(1)

2. Laine recorded the number of bedrooms in different houses on an estate.

The table shows her results.

 

Frequency Diagram GCSE Question 2

 

(a) Complete the vertical line chart to show Laine’s results.

 

 

(b) How many houses have at least 3 bedrooms?

 

(3 marks)

Show answer

(a)

 

Frequency Diagram GCSE Question 2a Image 2

(2)

 

(b)

 

30

(1)

3. Here is a frequency diagram showing the times of people solving a sudoku problem.

 

Frequency Diagram GCSE Question 3

 

(a)  Complete the grouped frequency table.

 

Frequency Diagram GCSE Question 3a Image 1

 

(b) How many people were there altogether who did the sudoku?

 

(3 marks)

Show answer

(a)

 

Frequency Diagram GCSE Question 3a Image 2

(2)

 

(b)

 

18

(1)

Learning checklist

You have now learned how to:

  • Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, and bar charts for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data.

The next lessons are

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