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? ### 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 (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.

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 ## 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:

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.

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:

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.

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:

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.

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:

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.

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:

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.

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.

### Practice frequency diagram questions

1. Choose the correct frequency table for the following frequency diagram:         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:         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:         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:         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:         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:         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. (a) Complete the bar chart to show Will’s results. (b) How many more sparrows than robins were there?

(3 marks)

(a) (2)

(b)

12

(1)

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

The table shows her results. (a) Complete the vertical line chart to show Laine’s results. (b) How many houses have at least 3 bedrooms?

(3 marks)

(a) (2)

(b)

30

(1)

3. Here is a frequency diagram showing the times of people solving a sudoku problem. (a)  Complete the grouped frequency table. (b) How many people were there altogether who did the sudoku?

(3 marks)

(a) (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.

## Still stuck?

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#### FREE GCSE maths practice papers (Edexcel, AQA & OCR)

8 sets of free exam practice papers written by maths teachers and examiners for Edexcel, AQA and OCR.

Each set of exam papers contains the three papers that your students will expect to find in their GCSE mathematics exam.