Using Two-Way Tables

## Using Two-Way Tables

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.

## Example 1

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

## Example 2

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