# Unit 1 Section 2 : Two Way Tables

In this section we introduce the idea of a two-way table, which we can use to present information about situations.

## Example Question

Emma has collected information about the cats and dogs that children in her class have as pets.
There are 30 pupils. For each pupil, there are four possible responses they could make:
• The pupil has a cat and a dog.
• The pupil has a cat but not a dog.
• The pupil has a dog but not a cat.
• The pupil does not have a cat or a dog.
This information can be represented in the table below.
 Has a dog Does not have a dog Has a cat These pupils have both a cat and a dog These pupils have a cat but not a dog Does not have a cat These pupils have a dog but not a cat These pupils do not have a cat or a dog

When Emma has entered some of her data, the table looks like this:
 Has a dog Does not have a dog Has a cat 8 4 Does not have a cat 12
Emma has missed out one of the numbers, but we know that there are 30 pupils in her class.

Practice Questions
Work out the answer to each of these questions then click on the button marked to see whether you are correct.

(a) How many pupils do not have a cat or a dog?

(b) How many pupils have a dog?

(c) How many pupils have a cat?

(d) How many children have at least one of these pets?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
People leaving a football match were asked if they supported Manchester United or Newcastle.
They were also asked if they were happy. The table below gives the results.
 Manchester United Newcastle Happy 40 8 Not Happy 2 20
(a) How many Manchester United supporters were happy?

(b) How many Newcastle supporters were asked the questions?

(c) How many Manchester United supporters were not happy?

(d) How many people were asked the questions in total?

Question 2
The children in a class conducted a survey to find out how many children had videos at home and how many had computers at home. Their results are given in the table below.
 Video No Video Computer 8 2 No Computer 20 3
(a) How many children did not have a video at home?

(b) How many children had a computer at home?

(c) How many children had neither item at home?

(d) How many children were in the class?

Question 3
The children in a school are to have extra swimming lessons if they cannot swim. The table below gives information about the children in Years 7, 8 and 9.
 Can swim Can not swim Year 7 120 60 Year 8 168 11 Year 9 172 3
(a) How many children need swimming lessons?

(b) How many children are there in Year 8?

(c) How many of the Year 7 children can not swim?

(d) How many children in Years 7 and 8 can swim?

(e) How many children are there altogether in Years 7, 8 and 9?

Question 4
40 children are members of a cycling club. Details of their bikes are given below. Each child has one bike.
 MountainBike RacingBike BMXBike 15-speed 2 0 0 12-speed 8 0 10-speed 1 8 0 1-speed 0 0 15
(a) Fill in the number of 12-speed racing bikes on the table.

(b) How many children have mountain bikes?

(c) Which type of bike is the most popular?

Question 5
The headteacher of a school with 484 pupils collected information about how many of the pupils wear glasses.
 Alwayswearglasses Sometimeswearglasses Neverwearglasses Boys 40 161 Girls 36 55 144
(a) Fill in the number of boys who sometimes wear glasses.

(b) How many pupils wear glasses some of the time?

(c) How many pupils never wear glasses?

(d) Are there more boys or girls in the school?

Question 6
During one month, exactly half of the 180 babies born in a hospital were boys, and 40 of the babies weighed 4 kg or more. There were 26 baby boys who weighed 4 kg or more.
 Less than 4kg 4kg or more Boys Girls
Complete the table on the left, using the information above.

Question 7
In a school survey pupils chose the TV programme they liked best from a list. Some of the results are given in the table below.
 Blue Peter Grange Hill Newsround Year 7 8 1 Year 8 12 5
The same number of pupils took part in Year 7 and Year 8.
Six pupils chose Newsround in total.

(a) Complete the table and then check:
(i) the number of Year 7 pupils who chose Grange Hill
(ii) the number of Year 8 pupils who chose Newsround

(c) Which programme was the most popular?

For these last two questions, you will need to draw your own two-way table on paper.

Question 8
In a car showroom there are 8 blue cars, one of which is a hatchback. 6 of the 20 cars in the showroom are hatchbacks.

How many cars are not hatchbacks and are not blue?

Question 9
In a class of 32 pupils, there were 8 girls who played hockey and 5 boys who did not.

How many boys played hockey if there were 15 girls in the class?

You have now completed Unit 1 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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