Two-way Tables
Get to grips with two-way tables using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on completing two-way tables, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Every row and column must add up to its total.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
A two-way table organises data by two different characteristics at once, with one shown in the rows and the other in the columns.
Each cell gives the frequency for a particular combination, such as the number of girls who walk to school. Totals appear in an extra row and column, and the grand total sits in the corner.
Those totals make the table self-checking. Each row must add to its row total, each column to its column total, and both sets must agree with the grand total. That property is what lets you fill in missing values.
Revision notes
Reading the table
Find the row for one characteristic and the column for the other, then read where they meet.
The cell where the row and column totals meet is the grand total, which equals the sum of all the individual cells.
Completing missing values
Subtract the known entries in a row or column from its total.
If a row totals \(45\) and two of its three entries are \(18\) and \(15\), the third is \(12\). Work through the rows and columns until everything is filled.
Using the table for probability
The probability of a combination is its cell frequency divided by the grand total.
If \(14\) of \(60\) students are girls who cycle, the probability of picking one at random is \(\frac{14}{60}\).
Key points
- A two-way table sorts data by two characteristics.
- Rows show one characteristic, columns the other.
- Each cell gives a combined frequency.
- Rows and columns must add to their totals.
- The grand total is the sum of all cells.
- Probability is the cell frequency over the grand total.
Worked examples
Example 1
A row totals \(50\) with entries \(21\) and \(17\) and one missing. Find the missing value.
Working
Example 2
A table has row totals \(30\) and \(45\). Find the grand total.
Working
Example 3
\(18\) of \(90\) students are boys who walk. Find the probability of picking one at random.
Working
Common mistakes
Adding the grand total again when summing cells.
The grand total is the sum of the cells, not another cell to include.
Confusing rows with columns.
Check the headings carefully before reading a value.
Using a row total as the denominator for a probability.
Unless the question restricts to that row, use the grand total.
Not checking the totals agree.
Rows and columns must both add to the grand total.
Exam tips
- Fill in missing values using the row and column totals.
- Check both directions agree with the grand total.
- Read the headings before taking any value.
- Use the grand total as the denominator unless told otherwise.
Key terms
- Two-way table
- A table sorting data by two characteristics.
- Grand total
- The total of all the cells.
- Cell
- One entry in the table.
- Frequency
- How many items fall into a category.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.