Two-way tables (Edexcel GCSE Maths): Revision Notes
Two-way tables
What are two-way tables?
Two-way tables are a way of organising data that shows the relationship between two different categories or variables. They display information in rows and columns, making it easy to see how different groups compare across different characteristics.
These tables are particularly useful for analysing survey data, comparing groups, or looking at how two different factors relate to each other. You can find missing information in two-way tables by using addition and subtraction.
Two-way tables are sometimes called contingency tables or cross-tabulation tables. They're essential tools in statistics and data analysis, helping us understand relationships between categorical variables.
Structure of two-way tables
Two-way tables have a clear structure that you need to understand:
- Rows run horizontally across the table and represent one category
- Columns run vertically down the table and represent another category
- Cells contain the actual data values where rows and columns meet
- Totals appear at the end of each row and column, plus a grand total in the bottom-right corner
For example, if you're looking at students' vegetarian choices across different year groups, the rows might show "Vegetarian" and "Not vegetarian", while the columns show "Year 7", "Year 8", and "Year 9".
Golden rules for two-way tables
There are two essential rules that always apply to two-way tables:
- Column rule: The numbers in each column must add up to the total for that column
- Row rule: The numbers in each row must add up to the total for that row
These golden rules help you find missing values and check that your completed table is correct.
How to complete missing values
When you need to fill in missing numbers in a two-way table, follow this systematic approach:
- Start with the grand total - write the total in the bottom right-hand cell if it's missing
- Look for easy calculations - find rows or columns that have only one missing number
- Use subtraction - if you know the total and most of the values, subtract the known values from the total
- Use addition - add up values to find totals when you have all the individual numbers
- Work systematically - fill in missing values as you go along, using each new number to help find the next
- Check your work - add up all row totals and all column totals to ensure they match the grand total
The key to success with two-way tables is patience and systematic working. Don't try to fill in multiple cells at once - work through one calculation at a time, and each completed cell will help you solve the next one.
Worked example walkthrough
Worked Example: Completing a Voting Survey Table
Let's see how this works with a voting survey example:
If you have a table showing how males and females voted for different parties:
Step 1: Labour column: Total is 53, Female is 21, so Male must be
Step 2: Female row: Total is 47, Labour is 21, Conservative is 13, so Other must be
Step 3: Conservative column: Female is 13, Male is 27, so total is
Continue this process until all cells are filled, then verify by checking that row totals and column totals add up to the same grand total.
Exam tips
- Always write down your calculations clearly to show your working
- Double-check by adding row totals and column totals separately
- Look for the simplest calculation first - start with rows or columns that need only one missing number
- Be systematic - don't jump around the table randomly
- Show your method even if you make arithmetic errors, as you can still get method marks
Remember that in exams, partial credit is often awarded for correct method even if your final answer is wrong due to an arithmetic error. Always show your working step by step.
Summary
Key Points to Remember:
- Two-way tables organise data by showing relationships between two different categories using rows and columns
- Golden rules: Row numbers add to row totals, column numbers add to column totals
- Find missing values by using addition and subtraction systematically
- Always check your work by verifying that all totals add up correctly
- Start with easy calculations and work through the table methodically