Two-way Tables & Venn Diagrams (Edexcel GCSE Statistics)

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

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 refers to the entire data set

  • So there are a total of 12+4+21+8=45 members in the sports club

• Occasionally, the numbers in the Venn diagram are not numbers of things or people, etc.

  • For example, the numbers might be percentages

    • In this case all the numbers in the Venn diagram must add up to 100%

  • Or the numbers might be probabilities

    • In this case all the numbers in the Venn diagram must add up to 1

How do I draw a Venn diagram?

• Start with a rectangle and overlapping circles

  • the number of circles needed will depend on how many characteristics you are dealing with

  • it will usually be 2 or 3

• To fill in the regions of your Venn diagram:

  • Work through each sentence/piece of information given in the question

  • Pieces of information may have to be combined before you can enter a value into the diagram

  • Not all values will be given directly

    • some may need working out

  • Remember to consider the words and and or