Venn diagrams are a type of diagram that uses circle to group and organise things, as seen below:
A Venn diagram is a helpful tool in displaying information about two categories, especially if things can be in both categories. Some Venn diagrams will use the diagram to sort the different objects. The one shown above uses numbers in each section to show how many objects fit into that section.
Some Venn diagrams wont have the outside box. Depending on the context this means that they are only considering the two circles or everything they are interested could be placed in at least one of the two circles.
A group of students were asked about their siblings. The two categories show if they have at least one brother, and if they have at least one sister.
How many of the students have at least one sibling?
How many of the students have at least one brother?
How many of the students don't have a sister?
Venn diagrams are a type of diagram that uses circles to group and organise things.
We can also use Venn diagrams with three circles. This uses the same concepts as a two circle Venn diagram but adds another circle which represents a third category. We can work things out in the same way, however there are more places the categories can overlap.
Joanne is struggling to decide what to watch online. She decides to pick one movie at random from the streaming website. A Venn diagram of her options sorts movies into three categories based on their genre: Comedy, Action and Horror.
How many of the movies are horror films?
How many of the movies fit into only one genre?
How many of the movies are an action film combined with at least one other genre?
Three circle Venn diagram is a diagram shows how components of three sets are related using three overlapping circles.
Two-way tables represent data that is classified by two criteria.
Right | Left | |
---|---|---|
Enjoys English | 4 | 9 |
Doesn't enjoy English | 2 | 15 |
To read a two-way table look at the column and row that a cell is in. For example there are 9 students who are left-handed and enjoy English, and 2 students who are right handed that don't enjoy English. Tables will often include totals of each column, row and the total sum. This is found by adding up every cell in that row or column.
Right | Left | Total | |
---|---|---|---|
Enjoys English | 4 | 9 | 13 |
Doesn't enjoy English | 2 | 15 | 17 |
Total | 6 | 24 | 30 |
The categories of the rows and columns should be chosen such that each person or object can only go in one of the cells.
This table describes the departures of trains out of a train station for the months of May and June.
Departed on time | Departed late | |
---|---|---|
May | 113 | 31 |
June | 108 | 33 |
How many trains departed during May and June?
What percentage of the trains in June were delayed? Write your answer as a percentage to one decimal place.
What fraction of the total number of trains during the 2 months were ones that departed on time in May?
Two-way tables represent data that is classified by two criteria.
A two-way table presents similar information as a Venn diagram. We can convert between a two-way table and a Venn diagram, and vice versa, by looking at which categories are represented by the Venn diagram or two-way table, and how the different regions or cells match up.
The number that is in both categories, 4 will go in the overlap of the two circles. The remaining value, 9, in the selected row, represents the "Entered and right-handed" students and will go into the "Entered" circle but not in the overlap because they are not "Left-handed". Any cells that are in neither the highlighted row nor the highlighted column will go into the surrounding box.
A student makes a Venn diagram of students who are late to school, and students who catch the bus to school.
Using the Venn diagram, complete the following table:
Late | Not late | |
---|---|---|
Caught bus | ||
Didn't catch bus |
We can convert between a two-way table and a Venn diagram by matching up their different parts.