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Sets and Venn diagrams

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Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

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3D Trigonometry - Higher

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Vectors - Higher

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Angles: types, notation and measuring

Basic angle rules

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Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

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Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Alice

Summary

Sets and Venn diagrams

In a nutshell

A set is a collection of 'things' known as elements. In statistics, sets are usually presented on a Venn diagram. This provides an easy way for the probability of an element, inside a given set, to be worked out.

Set theory

Sets are represented by a list of elements inside two curly brackets: { }

Example 1

The set of even numbers between $1$ and $10$ :

{ $2,4,6,8$ }
{ $x:$ $x$ is an even number between one and ten}

Venn diagrams representing sets

On a Venn diagram, each set is represented by a circle which contains all the elements within it.

Set Notation	Definition	Venn diagram Representation
n( $A$ )	Number of elements in set $A$ .
The empty set $\emptyset$	A set which has nothing in it.
Universal Set $\xi$ or $E$ or $U$	The set containing all elements.
Complement $A'$ or $\overline{A}$	All elements not in $A$ .
Intersection $A \cap B$	All elements in both $A$ and $B$ .
Union $A \cup B$	All elements in either $A$ or $B$ or both.
Conditional (A given B) $A\|B$	All elements in $A$ given they are in $B$ .
Disjoint sets	Two sets that share none of the same elements.
Subset $A \subset B$	$A$ is a set inside of $B$ .

Finding probabilities from Venn diagrams

You can use Venn diagrams to work out the probability of an event by counting the number of elements in the relevant set and taking that as a fraction out of the total.

Example 2

The Venn diagram shows the numbers of students that said they liked green and blue.

Maths; Statistics; KS4 Year 10; Sets and Venn diagrams

Find the probability that when selected at random, a pupil would like:

1. The colour green:

$\text{N(Year 11 Students)}= 100$

Work out the number of students that like green.

$\text{n}(G)= 20+23=43$

Work out the probability that a student likes green.

$\text{P(}G)= \frac{43}{100}$

2. Both blue and green:

Work out the number of students that like both blue and green.

$\text{n(}B\cap G)= 20$

Work out the probability that a student likes both blue and green.

$\text{P(}B \cap G)= \frac{20}{100}=\frac{1}{5}$

3. Blue given they like green:

Take the number of students that like both blue and green as a fraction out of the number that like green.

$\text{n(}G)=43 \\\text{ n(}B\cap G)= 20 \\\text{P(}B|G)=\frac{20}{43}$ 

Note: In the example above $25$ is the number of students that did not fit into either category - they did not like blue or green!

Learn with Basics

Length:

Unit 1

Listing outcomes

Unit 2

Venn diagrams

Jump Ahead

Optional

Unit 3

Sets and Venn diagrams

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What are disjoint sets?

Disjoint sets are two sets that share none of the same elements.

What is the union of two sets?

The union of two sets, A and B, is all the elements in A or B.

What is the intersect of two sets?

The intersect of two sets, A and B is all elements in both A and B.

What does the complement of A mean?

The complement is all elements not in A.

What is the universal set?

The universal set (ξ or E or U) is the set containing all elements.

How do I represent a set?

Sets are represented by a list of elements inside two curly brackets: { }.

What is a set?

A set is a collection of 'things' known as elements.

Home

Maths

Statistics

Sets and Venn diagrams

Videos

Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Alice

Summary

Sets and Venn diagrams

In a nutshell

Set theory

Sets are represented by a list of elements inside two curly brackets: { }

Example 1

The set of even numbers between $1$ and $10$ :

{ $2,4,6,8$ }
{ $x:$ $x$ is an even number between one and ten}

Venn diagrams representing sets

On a Venn diagram, each set is represented by a circle which contains all the elements within it.

Set Notation	Definition	Venn diagram Representation
n( $A$ )	Number of elements in set $A$ .
The empty set $\emptyset$	A set which has nothing in it.
Universal Set $\xi$ or $E$ or $U$	The set containing all elements.
Complement $A'$ or $\overline{A}$	All elements not in $A$ .
Intersection $A \cap B$	All elements in both $A$ and $B$ .
Union $A \cup B$	All elements in either $A$ or $B$ or both.
Conditional (A given B) $A\|B$	All elements in $A$ given they are in $B$ .
Disjoint sets	Two sets that share none of the same elements.
Subset $A \subset B$	$A$ is a set inside of $B$ .

Finding probabilities from Venn diagrams

You can use Venn diagrams to work out the probability of an event by counting the number of elements in the relevant set and taking that as a fraction out of the total.

Example 2

The Venn diagram shows the numbers of students that said they liked green and blue.

Find the probability that when selected at random, a pupil would like:

1. The colour green:

$\text{N(Year 11 Students)}= 100$

Work out the number of students that like green.

$\text{n}(G)= 20+23=43$

Work out the probability that a student likes green.

$\text{P(}G)= \frac{43}{100}$

2. Both blue and green:

Work out the number of students that like both blue and green.

$\text{n(}B\cap G)= 20$

Work out the probability that a student likes both blue and green.

$\text{P(}B \cap G)= \frac{20}{100}=\frac{1}{5}$

3. Blue given they like green:

Take the number of students that like both blue and green as a fraction out of the number that like green.

$\text{n(}G)=43 \\\text{ n(}B\cap G)= 20 \\\text{P(}B|G)=\frac{20}{43}$ 

Note: In the example above $25$ is the number of students that did not fit into either category - they did not like blue or green!

Learn with Basics

Length:

Unit 1

Listing outcomes

Unit 2

Venn diagrams

Jump Ahead

Optional

Unit 3

Sets and Venn diagrams

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What are disjoint sets?

Disjoint sets are two sets that share none of the same elements.

What is the union of two sets?

The union of two sets, A and B, is all the elements in A or B.

What is the intersect of two sets?

The intersect of two sets, A and B is all elements in both A and B.

What does the complement of A mean?

The complement is all elements not in A.

What is the universal set?

The universal set (ξ or E or U) is the set containing all elements.

How do I represent a set?

Sets are represented by a list of elements inside two curly brackets: { }.

What is a set?

A set is a collection of 'things' known as elements.

Sets and Venn diagrams

Videos

Summary

Exercises

Select Lesson

Exam Board

Statistics

Probability

Trigonometry

Angles and geometry

Shapes and area

Ratio proportion and rates of change

Graphs

Algebra

Number

Explainer Video

Summary

Sets and Venn diagrams

​​In a nutshell

Set theory

Example 1

Venn diagrams representing sets

Set Notation

Definition

Venn diagram Representation

Finding probabilities from Venn diagrams

Example 2

Learn with Basics

Unit 1

Listing outcomes

Unit 2

Venn diagrams

Jump Ahead

Unit 3

Sets and Venn diagrams

Final Test

FAQs - Frequently Asked Questions

What are disjoint sets?

What is the union of two sets?

What is the intersect of two sets?

What does the complement of A mean?

What is the universal set?

How do I represent a set?

What is a set?

Sets and Venn diagrams

Videos

Summary

Exercises

Select Lesson

Exam Board

Statistics

Probability

Trigonometry

Angles and geometry

Shapes and area

Ratio proportion and rates of change

Graphs

Algebra

Number

Explainer Video

Summary

Sets and Venn diagrams

​​In a nutshell

Set theory

Example 1

Venn diagrams representing sets

Set Notation

Definition

Venn diagram Representation

Finding probabilities from Venn diagrams

Example 2

Learn with Basics

Unit 1

Listing outcomes

Unit 2

Venn diagrams

Jump Ahead

Unit 3

Sets and Venn diagrams

Final Test

In a nutshell

In a nutshell