Two Way Tables in Statistics

In this worksheet, students practise completing and using two way tables.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Interpreting and Representing Data

Difficulty level:

QUESTION 1 of 10

It is common in the GCSE exam that questions come up where you are given information about two variables (i.e. Gender and favourite sport) and you are asked to work out the value of one specific part of this information (i.e. How many men like football)

To solve these questions, the easiest way is to use a two-way table.

Example 1: Complete the two way table.

 Blue Brown Green Total Male 6 3 14 Female 5 Total 8 30

To complete this, we just need to make each row and colum add up to the total that is given.

To start, we need to find the row or column that has only one missing.

If you keep repeating this, eventually you will get...

 Blue Brown Green Total Male 6 5 3 14 Female 6 5 5 16 Total 12 10 8 30

Example 2:

100 people are asked if they swim, cycle or run.

40 of the people were female

26 of the 47 runners were female

30 people swim

10 men were cyclists

a) Find the amount of people who cycled.

Step 1 here is to draw a two-way table and enter the totals that we know.

 Swim Run Cycle Total Male 10 Female 26 40 Total 30 47 100

Once we have this, we can fill in the rest of the information...

 Swim Run Cycle Total Male 29 21 10 60 Female 1 26 13 40 Total 30 47 23 100

From this, it is quite easy to see that the total amount of cyclists is 23.

b) Given that I choose a woman, what is the probability she will be a runner?

Be careful with this one, we are limiting this to women only so the probability will be out of 40.

26 of the women are runners which makes our probability 26/40 which cancels to 13/20

Complete the following two way table.

 Left Handed Right Handed Total Male 10 C D Female A 15 E Total B 30 50

 Value A B C D E

Pupils in year 7 and 8 were asked if they had siblings.

How many Year 8 pupils were asked in total?

 Yes No Total Year 7 16 Year 8 12 Total 30 70

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 C 20 Blonde A 20 E Black 16 D F Total B 60 100

Match the letter with the amount.

Column B

A
12
b
40
C
32
D
32
E
8
F
48

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 20 Blonde 20 Black 16 Total 60 100

I pick one person at random, find the probability that the person is a female with brown hair.

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 20 Blonde 20 Black 16 Total 60 100

I pick a man at random, what is the probability her has red hair?

75 people are asked for their gender and if they are right or left handed.

26 of the 50 right handed people were women.

15 men are left handed.

Find the amount of men who were asked.

100 pupils across Years 7 and 8 were asked if they had siblings

41 out of the 59 Year 8 pupils has siblings

20 Year 7 pupils were only children,

How many year 7 pupils have siblings?

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

Using the two way table shown, find the amount of red haired people were surveyed.

 Red Blonde Brown Total Male Female Total

Step 1: Draw a table and put in the information you know.

 Red Blonde Brown Total Male 17 21 50 Female 92 150 Total 50 200

Step 2: Fill in the rest of the information.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

If I pick a person at random, what is the probability t will be a brown haired man?

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

If I pick a red haired person, what is the probability he has red hair?

• Question 1

Complete the following two way table.

 Left Handed Right Handed Total Male 10 C D Female A 15 E Total B 30 50

 Value A B C D E
EDDIE SAYS
Remember to look for the rows or columns that have only one missing, for this, you can either start with the right-handed people or the total on the bottom.
• Question 2

Pupils in year 7 and 8 were asked if they had siblings.

How many Year 8 pupils were asked in total?

 Yes No Total Year 7 16 Year 8 12 Total 30 70

36
EDDIE SAYS

If you complete the table correctly, you should get...

 Yes No Total Year 7 16 18 34 Year 8 24 12 36 Total 40 30 70

From this, we can see that the number of Year 8 pupils is...

• Question 3

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 C 20 Blonde A 20 E Black 16 D F Total B 60 100

Match the letter with the amount.

Column B

A
12
b
40
C
8
D
32
E
32
F
48
EDDIE SAYS

Remembering that we need to start with the row or column wheere we are only missing one piece of information,

Completing the table correctly should give...

 Male Female Total Red 12 8 20 Blonde 12 20 32 Black 16 32 48 Total 40 60 100
• Question 4

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 20 Blonde 20 Black 16 Total 60 100

I pick one person at random, find the probability that the person is a female with brown hair.

32/100
16/50
8/25
EDDIE SAYS

Remembering that we need to start with the row or column wheere we are only missing one piece of information,

Completing the table correctly should give...

 Male Female Total Red 12 8 20 Blonde 12 20 32 Black 16 32 48 Total 40 60 100
We can now see that there are 32 brown haired female out of the 100 in total.
• Question 5

Male and female students hair colours were recorded in a two way table.

 Male Female Total Red 12 20 Blonde 20 Black 16 Total 60 100

I pick a man at random, what is the probability her has red hair?

12/40
6/20
3/10
EDDIE SAYS

Remembering that we need to start with the row or column wheere we are only missing one piece of information,

Completing the table correctly should give...

 Male Female Total Red 12 8 20 Blonde 12 20 32 Black 16 32 48 Total 40 60 100
The question states that we are picking out men. This means we are limited to 40. 12 of them are red haired.
• Question 6

75 people are asked for their gender and if they are right or left handed.

26 of the 50 right handed people were women.

15 men are left handed.

Find the amount of men who were asked.

39
EDDIE SAYS

Step 1: Draw a table and put in the information you know.

 LH RH Total M 15 F 26 Total 50 75

Step 2: Fill in the rest of the information.

 LH RH Total M 15 24 39 F 10 26 36 Total 25 50 75

• Question 7

100 pupils across Years 7 and 8 were asked if they had siblings

41 out of the 59 Year 8 pupils has siblings

20 Year 7 pupils were only children,

How many year 7 pupils have siblings?

21
EDDIE SAYS

Step 1: Draw a table and put in the information you know.

 Y N Total Yr 7 20 Yr 8 41 59 Total 100

Step 2: Fill in the rest of the information.

 Y N Total Yr 7 21 20 41 Yr 8 41 18 59 Total 62 38 100

• Question 8

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

Using the two way table shown, find the amount of red haired people were surveyed.

 Red Blonde Brown Total Male Female Total

Step 1: Draw a table and put in the information you know.

 Red Blonde Brown Total Male 17 21 50 Female 92 150 Total 50 200

Step 2: Fill in the rest of the information.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

46
EDDIE SAYS

Step 1: Draw a table and put in the information you know.

 Red Blonde Brown Total Male 17 21 50 Female 92 150 Total 50 200

Step 2: Fill in the rest of the information.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

• Question 9

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

If I pick a person at random, what is the probability t will be a brown haired man?

12/200
6/100
3/50
EDDIE SAYS
If we interrogate the table, we can see we have 12 brown-haired men out of 200. This can then just be written as a probability and then cancelled
• Question 10

200 people are surveyed about their hair colour

3 times as many women as men were asked.

There were 17 men with red hair

50 people had blonde hair, 21 of these were male.

 Red Blonde Brown Total Male 17 21 12 50 Female 29 29 92 150 Total 46 50 108 200

If I pick a red haired person, what is the probability he has red hair?

17/46
EDDIE SAYS
Did you notice the limit here? We're only looking at the red-haired people so we're picking out of 46. If we interrogate the table, we can see we have 17 red-haired men out of 46. This can then just be written as a probability but cannot be cancelled.
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