Exam code:1ST0
Two-way Tables
What are two-way tables?
-
Two-way tables are tables that compare two types of characteristics
-
For example, a college of 55 students has
-
two year groups (Year 12 and Year 13)
-
and two language options (Spanish and German)
-
-
The two-way table for the college’s data is shown:
Spanish
German
Year 12
15
10
Year 13
5
25
-
How do I interpret a two-way table?
-
Draw in the totals of each row and column
-
Include an overall total in the bottom-right corner
-
It should be the sum of the totals above it, or to its left
-
(Both should be the same – if they are not the same there is a mistake somewhere!)
-
-
-
For the example above:
Spanish
German
Total
Year 12
15
10
25
Year 13
5
25
30
Total
20
35
55
-
Now we know that there are 25 students in Year 12 and 30 in Year 13
-
And that there are 20 students who study Spanish and 35 who study German
-
Examiner Tips and Tricks
-
Check that your row and column totals add up to the overall total
-
Otherwise anything else you calculate from the table will be wrong!
-
Worked Example
At an art group, children are allowed to choose between colouring, painting, clay modelling and sketching.
A total of 60 children attend and are split into two classes: class A and class B.
12 of class A chose the activity colouring and 13 of class B chose clay modelling.
A total of 20 children chose painting and a total of 15 chose clay modelling.
8 of the 30 children in class A and 4 of the children in class B chose sketching.
Construct a two-way table to show this information.
Read through each sentence and fill in the numbers that are given
|
Colouring |
Painting |
Clay modelling |
Sketching |
Total |
|
|
Class A |
12 |
8 |
30 |
||
|
Class B |
13 |
4 |
|||
|
Total |
20 |
15 |
60 |
Use the row and column totals to fill in any obvious missing numbers
|
Colouring |
Painting |
Clay modelling |
Sketching |
Total |
|
|
Class A |
12 |
15 – 13 = 2 |
8 |
30 |
|
|
Class B |
13 |
4 |
60 – 30 = 30 |
||
|
Total |
20 |
15 |
8 + 4 = 12 |
60 |
Use the row and column totals again to find the last few numbers
|
Colouring |
Painting |
Clay modelling |
Sketching |
Total |
|
|
Class A |
12 |
30 – 12 – 2 – 8 = 8 |
2 |
8 |
30 |
|
Class B |
30 – 12 – 13 – 4 = 1 |
20 – 8 = 12 |
13 |
4 |
30 |
|
Total |
12 + 1 = 13 |
20 |
15 |
12 |
60 |
Write out your final answer
|
Colouring |
Painting |
Clay modelling |
Sketching |
Total |
|
|
Class A |
12 |
8 |
2 |
8 |
30 |
|
Class B |
1 |
12 |
13 |
4 |
30 |
|
Total |
13 |
20 |
15 |
12 |
60 |
Venn Diagrams
What is a Venn diagram?
-
Venn diagrams allow us to show two (or more) characteristics of a situation where there is overlap between the characteristics
-
For example, students in a sixth form college can study biology or chemistry
-
but there may be students who study both
-
or students who study neither
-
-
How do I interpret a Venn diagram?
-
Each region in a Venn diagram represents a different part of the data
-
The numbers in the circle labelled ‘A‘ tell us how many items belong to ‘set A’ in the data
-
For example this might be the members of a sports club who like Archery
-
The diagram tells us that there are 12+4=16 members who like archery
-
-
The numbers in the circle labelled ‘B‘ tell us how many items belong to ‘set B’ in the data
-
For example this might be the members of a sports club who like Badminton
-
The diagram tells us that there are 4+21=25 members who like badminton
-
-
The region where the two circles overlap tell us how many items are in set A and set B
-
So this would be members of the club who like Archery and Badminton
-
The diagram tells us that there are 4 of these
-
-
The two circles together tell us how many items are in set A or set B
-
So this would be members of the club who like Archery or Badminton
-
The diagram tells us that there are 12+4+21=37 of these
-
Note that ‘set A or set B’ includes items that are in both sets
-
-
The area outside the two circles tells us how many items are not in set A and not in set B
-
This would be the members of the club who don’t like Archery and don’t like Badminton
-
The ‘8’ tells us that there are 8 of these
-
-
The rectangle around the diagram
Responses