A Two-way Table is used to show totals of a population with two different properties, or pieces of information. For example, students in a school can be totalled by year group and by male/female.
Two-way tables can be added vertically to obtain column totals; and horizontally to obtain row totals. The row totals can be added together to obtain a grand total. This should be the same as the column totals added together.
A school is taking a large group of students on an exchange trip. Complete the table, filling in any missing entries, and give the total number of teachers that will be on the trip.
| Year 7 | Year 8 | Year 9 | Year 10 | Year 11 | TOTAL | |
| Teachers | 1 | 3 | ||||
| Girls | 8 | 7 | 6 | 36 | ||
| Boys | 3 | 5 | 11 | 27 | ||
| TOTAL | 13 | 12 | 12 | 21 | 12 | 70 |
Each time, find a row or column missing one item. Subtract the other numbers in that row or column from the row/column total to find the missing answer.
| Year 7 | Year 8 | Year 9 | Year 10 | Year 11 | TOTAL | |
| Teachers | 1 | 2 | 1 | 3 | 0 | 7 |
| Girls | 8 | 7 | 6 | 7 | 8 | 36 |
| Boys | 4 | 3 | 5 | 11 | 4 | 27 |
| TOTAL | 13 | 12 | 12 | 21 | 12 | 70 |
Calculations:
Year 7 Boys. Use column total:13 - 8 - 1 = 4
Year 11 Boys. Use Row total: 27 - 4 - 3 - 5 - 11 = 4
Similarly, Year 8, Year 9 teachers and Year 10 girls: use column totals
Year 11 girls, use row totals
Year 11 teachers: use column totals
Add the teachers for a total
Answer: Total number of teachers: 7
A car showroom has 35 cars in total. There are 6 blue cars, 11 are black and the remainder are red. There are three styles: 10 are 3-door cars, 13 are 5-door cars and 12 are SUVs.
Of the 3-door cars, 2 are black and 3 are silver. Of the red cars, 7 are 5-door, Of the SUVs, 3 are silver. How many black SUVs does the car showroom have?
Complete the table given the information in the question.
| 3-door | 5-door | SUV | TOTAL | |
| Black | 2 | 6 | ||
| Silver | 3 | 3 | 11 | |
| Red | 7 | 18 | ||
| TOTAL | 10 | 13 | 12 | 35 |
Then determine the missing values:
| 3-door | 5-door | SUV | TOTAL | |
| Black | 2 | 1 | 3 | 6 |
| Silver | 3 | 5 | 3 | 11 |
| Red | 5 | 7 | 6 | 18 |
| TOTAL | 10 | 13 | 12 | 35 |
Answer: 3