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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.

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.

**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 **represent data by drawing straight lines to a given frequency.

They can be used for ungrouped numerical data.

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)

In order to draw a frequency diagram:

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

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

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

DOWNLOAD FREEDraw 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.

2**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.

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.

Draw a vertical line chart for this data:

**Draw a pair of axes and label them.**

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

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

Draw a vertical line chart for this data:

**Draw a pair of axes and label them.**

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

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

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.

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.

**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.

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.

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)**

Show answer

(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)**

Show answer

(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)**

Show answer

(a)

**(2)**

(b)

18

**(1)**

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.

- Frequency polygons
- Pie charts
- Histograms
- Scatter diagrams
- Cumulative frequency graphs
- Mean from a frequency table
- Quartiles
- Box plots

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