Using Two-Way Tables

# Using Two-Way Tables

GCSE(F), GCSE(H),

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 used to compare the distribution of a population or to determine probabilities.

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.

## Examples

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 7Year 8Year 9Year 10Year 11TOTAL
Teachers13
Girls87636
Boys351127
TOTAL131212211270

Answer: Total number of teachers: 7

Year 7Year 8Year 9Year 10Year 11TOTAL
Teachers121307
Girls8767836
Boys43511427
TOTAL131212211270

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

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 door5 doorSUVTOTAL
Black26
Silver3311
Red718
TOTAL10131235

Then determine the missing values:

3 door5 doorSUVTOTAL
Black2136
Silver35311
Red57618
TOTAL10131235