GCSE Maths Statistics

Representing Data

Frequency Polygon

Frequency Polygon

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

There are also frequency polygon 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 polygon?

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 polygons are used to display data and show the frequency distribution over a continuous scale.

To construct a frequency polygon we need to know the value for the frequency of each group. 

For example,

Below is an example of a frequency polygon, with the associated data table.

Frequency Polygon Image 1

Frequency Polygon Image 2

The grouped data is presented as a continuous scale on the horizontal axis – we do not show the exact class intervals on the graph.

frequency polygons image 3

Step-by-step guide: Frequency diagrams

What is a frequency polygon?

What is a frequency polygon?

How to draw a frequency polygon

In order to draw a frequency polygon:

  1. Calculate the midpoint of each class interval.
  2. Plot the class frequency at the midpoint for the class.
  3. Connect the plotted values using straight line segments.

Explain how to draw a frequency polygon

Explain how to draw a frequency polygon

Frequency polygons worksheet

Frequency polygons worksheet

Frequency polygons worksheet

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

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Frequency polygons worksheet

Frequency polygons worksheet

Frequency polygons worksheet

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

DOWNLOAD FREE

Frequency polygon examples

Example 1: standard problem

The length L\;cm of 16 carrots were measured and recorded into a grouped frequency table.

frequency polygons example 1 Image 1

Draw a frequency polygon to represent the grouped data. Use the axes below.

frequency polygons example 1 Image 2

  1. Calculate the midpoint of each class interval.

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.

frequency polygons example 1 step 1

2Plot the class frequency at the midpoint for the class.

The midpoints are the x -coordinate and the frequencies are the y -coordinate.

frequency polygons example 1 step 2

Frequency Polygon Example 1 Step 2 Image 2

3Connect the plotted values using straight line segments.

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.

Frequency Polygon Example 1 Step 3

Example 2: large class intervals

18 students were asked to hop on one leg as far as they can in 3 minutes. The results were grouped into the table below.

frequency polygons example 2 Image 1

Draw a frequency polygon on the axes provided to represent this data.

frequency polygons example 2 Image 2

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2 .


frequency polygons example 2 step 1

The midpoints are the x -coordinate and the frequencies are the y -coordinate.


frequency polygons example 2 step 2 image 1


frequency polygons example 2 step 2 image 2

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.


Example 3: standard problem

Draw a frequency polygon for the following grouped data on the axes provided showing the average speed of vehicles travelling down a road.

frequency polygons example 3 image 1

frequency polygons example 3 image 2

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2 .


frequency polygons example 3 step 1

The midpoints are the x -coordinate and the frequencies are the y -coordinate.


frequency polygons example 3 step 2


Frequency Polygon Example 3 Step 2 Image 2

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.


Frequency Polygon Example 3 Step 3

Example 4: worded problem

An electrician is measuring the output voltage of plug sockets. He collects the data into groups shown in the table below.

frequency polygons example 4 image 1

Draw a frequency polygon to represent the data on the set of axes below.

frequency polygons example 4 image 2

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2 .


frequency polygons example 4 step 1

The midpoints are the x -coordinate and the frequencies are the y -coordinate.


frequency polygons example 4 step 2 image 1


frequency polygons example 4 step 2 image 2

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.


frequency polygons example 4 step 3

Example 5: standard problem – 5 rows

Data for the test score as a percentage is given in the table below.

frequency polygons example 5 image 1

Use the set of axes below to draw a frequency polygon for the data. Label each axis.

frequency polygons example 5 image 2

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2 .


frequency polygons example 5 step 1

The midpoints are the x -coordinate and the frequencies are the y -coordinate.


frequency polygons example 5 step 2


Frequency Polygon Example 5 Step 2 Image 2


Don’t forget to label the axes titles as well.

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.


Frequency Polygon Example 5 Step 3

Example 6: different class intervals

The time T seconds for a raft of penguins to dive into water from a ledge was recorded in a grouped frequency table below. Draw a frequency polygon on the axes below for the following grouped data.

frequency polygons example 6 image 1

frequency polygons example 6 image 2

The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2 .


frequency polygons example 6 step 1

The midpoints are the x -coordinate and the frequencies are the y -coordinate.


frequency polygons example 6 step 2 image 1


frequency polygons example 6 step 2 image 2

Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.


frequency polygons example 6 step 3

Common misconceptions

  • Joining the points

Do not join the last point to the first point.

frequency polygons common misconceptions image

  • Using the endpoints, not the midpoints

The coordinate must be plotted at the centre of each class interval, at the given frequency.

  • 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. The midpoint can be a decimal.

  • Straight line segments only

The coordinates of a frequency polygon are joined using a straight line segment. Do not connect them using freehand or draw them curved like a cumulative frequency curve; they should be drawn using a ruler!

  • The graph is not a frequency polygon

A frequency polygon is a specific type of frequency diagram. Do not draw a bar chart or a vertical line diagram – they are not distinctly frequency polygons.

Practice frequency polygon questions

1. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 1 image 1

frequency polygons practice questions 1 image 2

GCSE Quiz False

frequency polygons practice questions 1 image 3

GCSE Quiz True

frequency polygons practice questions 1 image 4

GCSE Quiz False

frequency polygons practice questions 1 image 5

GCSE Quiz False

frequency polygons practice questions 1 explanation image

 

Plotting the coordinates and joining them with straight line segments, we get

 

frequency polygons practice question 1 image 3

2. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 2 image 1

frequency polygons practice questions 2 image 2

GCSE Quiz False

frequency polygons practice questions 2 image 3

GCSE Quiz False

frequency polygons practice questions 2 image 4

GCSE Quiz False

frequency polygons practice questions 2 image 6

GCSE Quiz True

frequency polygons practice questions 2 explanation image

 

Plotting the coordinates and connecting them using straight line segments, we get

 

frequency polygons practice question 2 image 5 answer

3. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 3 image 1

GCSE Quiz False

frequency polygons practice questions 3 image 3

GCSE Quiz False

frequency polygons practice questions 3 image 4

GCSE Quiz True

frequency polygons practice questions 3 image 5

GCSE Quiz False

frequency polygons practice questions 3 explanation image

 

These coordinates need joining up with straight line segments to achieve the solution.

 

frequency polygons practice questions 3 image 4

4. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 4 image 1

frequency polygons practice questions 4 image 2

GCSE Quiz True

frequency polygons practice questions 4 image 3

GCSE Quiz False

frequency polygons practice questions 4 image 4

GCSE Quiz False

frequency polygons practice questions 4 image 5

GCSE Quiz False

frequency polygons practice questions 4 explanation image 1

 

These coordinates need joining up with straight line segments to get the solution.

 

 

frequency polygons practice questions 4 explanation image 2

5. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 5 image 2

GCSE Quiz False

frequency polygons practice questions 5 image 3

GCSE Quiz True

frequency polygons practice questions 5 image 4

GCSE Quiz False

frequency polygons practice questions 5 image 5

GCSE Quiz False

 

Each coordinate is to be plotted and connected with a straight line segment to the next coordinate.

 

frequency polygons practice question 5 explanation

6. Which is the correct frequency polygon for the grouped frequency table?

 

frequency polygons practice questions 6 image 1

frequency polygons practice questions 6 image 2

GCSE Quiz False

frequency polygons practice questions 6 image 3

GCSE Quiz True

frequency polygons practice questions 6 image 4

GCSE Quiz False

frequency polygons practice questions 6 image 5

GCSE Quiz False

frequency polygons practice questions 6 explanation image

 

These need joining up with straight line segments to get the solution.

 

frequency polygons practice question 6 image 3 answer

Frequency polygon GCSE questions

1. The frequency table shows some information about 54 test scores.

 

Frequency Polygon Example 5

 

On the grid, draw a frequency polygon for the information in the table.

 

Frequency Polygon GCSE Question 1 Image 2

 

(3 marks)

Show answer

Midpoints: 10, 30, 50, 70 and 90.

(1)

 

Frequency Polygon GCSE Question 1 Image 3

 

All coordinates plotted accurately.

(1)

All coordinates connected with a straight line segment.

(1)

2. A farmer weighs 50 potatoes.

The frequency table shows the information.

 

Frequency Polygon GCSE Question 2 Image 1

 

On the grid, draw a frequency polygon for the information in the table.

 

Frequency Polygon GCSE Question 2 Image 2

 

(3 marks)

Show answer

Midpoints: 20, 40, 60, 80 and 100.

(1)

 

Frequency Polygon GCSE Question 2 Image 3

 

All coordinates plotted accurately.

(1)

All coordinates connected with a straight line segment.

(1)

3. The frequency table shows some information about the heights of 80 plants.

 

frequency polygons GCSE question 3

 

On the grid, draw a frequency polygon for the information in the table.

 

Frequency Polygon GCSE Question 3 Image 2

 

(3 marks)

Show answer

Midpoints: 5, 15, 25, 35, 45 and 55.

(1)

 

Frequency Polygon GCSE Question 3 Image 3

 

All coordinates plotted accurately.

(1)

All coordinates connected with a straight line segment.

(1)

Learning checklist

You have now learned how to:

  • Interpret and present discrete and continuous data using appropriate graphical methods (frequency polygons)

The next lessons are

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