Two-way tables

Part of MathsCollecting and recording data

Key points

An image of a two way table.
A two-way table showing the languages studied by year group.

  • can be represented in many ways. Two-way tables are a common representation of data as they are easy to read and show the of two .

  • In two-way tables, the rows represent one variable, and the columns represent another. Each represents the frequency of data points that fit both variables.

An image of a two way table.
A two-way table showing the languages studied by year group.
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Using two-way tables

  • A two-way table shows the frequency of data which satisfies two variables.

  • Each row represents one variable, and each column represents another. To read them, the cell which sits between the two will have the frequency of data points that fit both variables.

  • This two-way table summarises data collected about age and whether someone is left or right-handed.

    • To find the number of 12-year-olds who are right-handed in this two-way table, look for the cell which sits on the row for '12-year-olds' and in the column for 'right-handed':
An image of a two way table.

The frequencies show that 17 of the 12-year-olds are right-handed.

Examples

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  1. Example one. Reading a two way table. An image of a two way table. The table has two columns and two rows. The first column is labelled, walk. The second column is labelled, bus. The first row is labelled, year seven. The second row is labelled, year eight. The four cells have been populated with numbers. Reading left to right, the first row is: twenty five, seventeen. The second row is: twelve, thirty one. An additional column to the right, and an additional row below have been added to the table to represent the totals. These are both labelled total. These cells have been populated with numbers such that the additional column is, forty two, forty three, and eighty five. The additional row is, thirty seven, forty eight, and eighty five. The cells with the labels, walk, bus, year seven, and year eight are highlighted purple. The cells with the label, total, are highlighted orange. The eighty five is coloured orange.

    85 students were asked how they get to school. The results are shown in this two-way table.

Question

60 sports fans in two different towns were asked if they preferred football or rugby.

How many fans from Town 2 prefer rugby?

An image of a two way table. The table has two columns and two rows. The first column is labelled, football. The second column is labelled, rugby. The first row is labelled, town one. The second row is labelled, town two. The four cells have been populated with numbers. Reading left to right, the first row is: twenty one, twenty. The second row is: sixteen, three. The cells with the labels, football, rugby, town one, and town two are highlighted purple.

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Practise using two-way tables

Quiz

Practise interpreting two-way tables and using a two-way table to record information with this quiz. You may need a pen and paper to help you with your answers.

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Real-life maths

In sport, the position of different teams are sorted into a two-way table according to their success rate and other facts about their overall performance.

For example, football league tables are two-way tables in which each row represents a team, and each column represents different statistics about that team. This could be the total points scored or the number of games played, for example.

Two-way tables are used for this as they can show a large amount of information at once, which is easy to read and understand.

An image of a football league table.
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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.

Play the Divided Islands game!
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