Two Way Tables
What are two-way tables?
- Two-way tables allow us to consider two characteristics within a set of data
- For example, we may be interested in the number of students studying Spanish or German
- We may also be interested in how many of those students are in year 12 and how many are in year 13
- Spanish/German would be one characteristic in the two-way table, year 12/13 would be the second
- For example, we may be interested in the number of students studying Spanish or German
- One of the characteristics will be represented by the columns, the other by the rows
- A two-way table should include row totals and column totals
- The row/column totals are sometimes called marginal (or sub-) totals
- Where the row totals and column totals meet, we have the grand total
- Marginal totals can be really useful in two-way table questions
- If they're not mentioned, or not included in a given table, add them in!
- The row/column totals are sometimes called marginal (or sub-) totals
How do I draw and complete a two-way table?
- To construct a two-way table from information given in words in a question
- identify the two characteristics
- use rows for one characteristic and columns for the other
- add an extra row and column for the marginal totals (and grand total)
- Work your way through each sentence in the question
- fill in any values you can directly from the information given
- be prepared to come back to any information that cannot be put into the two-way table directly
- some information may need combining in order to deduce a value
Exam Tip
- Work carefully when completing a two-way table
- double check your values add up to each row/column total
- check your totals add up to the grand total
Worked example
At an art group children are allowed to choose between four activities; colouring, painting, clay modelling and sketching.
There is a total of 60 children attending the art group. 12 of the boys chose the activity colouring.
A total of 20 children chose painting and a total of 15 chose clay modelling. 13 girls chose clay modelling.
8 of the 30 boys chose sketching, as did 4 of the girls.
Construct a two-way table to show this information.
Construct the table carefully, remember to include marginal totals for the rows and columns.
Work through each sentence in turn, placing a value in the table where possible and coming back later to a sentence if need be.
Once those values are in place, work your way around the rest of the table until it is complete.
If you find you can't complete the table, look back at the question for some information you may have missed.
| Colouring | Painting | Clay modelling | Sketching | Total | |
| Boys | 12 | 30 - 12 - 2 - 8 = 8 | 15 - 13 = 2 | 8 | 30 |
| Girls | 30 - 12 - 13 - 4 = 1 | 20 - 8 = 12 | 13 | 4 | 60 - 30 = 30 |
| Total | 12 + 1 = 13 | 20 | 15 | 8 + 4 = 12 | 60 |
So the final two-way table is
| Colouring | Painting | Clay modelling | Sketching | Total | |
| Boys | 12 | 8 | 2 | 8 | 30 |
| Girls | 1 | 12 | 13 | 4 | 30 |
| Total | 13 | 20 | 15 | 12 | 60 |
You can do a quick check of your table values by ensuring the marginal totals add up to the grand total.
