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Two-Way Tables

FoundationHigherAQAEdexcel

Understand Two-Way Tables for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Two-way tables show the frequencies of two categorical variables at the same time.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A two-way table shows the frequencies for two categorical variables at the same time, with one variable across the columns and the other down the rows.

Each cell gives the frequency for one combination of the two categories. Row totals, column totals and the overall total appear in the margins, and the row totals and column totals must both add to the same overall total.

Missing values are found by subtraction, using the totals. If a row total is 40 and two of its three cells are 15 and 12, the third is \(40 - 15 - 12 = 13\). Working systematically from the totals inwards solves almost every two-way table question.

Revision notes

Reading the table

One variable runs across the columns and the other down the rows.

Each cell gives the frequency for that combination. The margins hold the row totals, column totals and the overall total.

Finding missing values

Use subtraction with the totals. A row total minus the known cells in that row gives the missing one.

Work systematically: fill in any row or column with only one missing value, which then often makes another row or column solvable.

Checking the table

The row totals must add to the overall total, and so must the column totals.

If they do not match, an error has been made. This check should be carried out on every completed table.

Key points

  • Two-way tables show two variables at once.
  • Each cell gives one combination's frequency.
  • Margins contain row and column totals.
  • Missing values are found by subtraction.
  • Row totals must sum to the overall total.
  • Column totals must sum to the same overall total.

Worked examples

Example 1

A row has a total of 40 and contains the values 15 and 12. Work out the missing value. [2 marks]

Working

\(40 - 15 = 25\)subtract the first known value from the total
\(25 - 12 = 13\)subtract the second known value

Example 2

A two-way table has row totals 30, 45 and 25. Work out the overall total. [1 mark]

Working

\(30 + 45 + 25 = 100\)add the row totals

Example 3

Explain how you can check that a completed two-way table is correct. [2 marks]

Working

Add the row totals and add the column totals separatelystate the check
Both should give the same overall total, and any difference shows an error has been madestate what the result means

Common mistakes

  • Adding when you should subtract.

    Missing cells are found by subtracting known values from the total.

  • Not checking both row and column totals.

    Both must give the same overall total.

  • Reading a cell as a total.

    Totals appear in the margins, not in the body of the table.

  • Filling cells in a row with two unknowns.

    Find a row or column with only one missing value first.

Exam tips

  • Start with any row or column having one missing value.
  • Check row and column totals both give the overall total.
  • Show each subtraction as a separate step.
  • Read the margins carefully to identify the totals.

Key terms

Two-way table
A table showing frequencies for two variables.
Cell
One entry giving a frequency for a combination.
Row total
The sum of the frequencies in one row.
Overall total
The sum of all frequencies in the table.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.