Top Rated by Parents/Students Nationwide

Pie Charts

Pie Charts

What is a pie chart?

  • A pie chart is a circle which is divided into slices (sectors) to show proportion
  • They show the relative size of categories of data compared to each other, rather than their actual size or number
    • For example if we were looking at the proportions of men and women working in a company, we are more interested in the relative sizes than the actual numbers of men and women
  • There are 360°  in a circle, and we can use this to help us calculate the size of each slice of the pie chart

How do I draw a pie chart?

  • This is shown easiest through an example
  • The following data is collected for a class of 30 students about their favourite colour

Colour

Red

Purple

Blue

Green

Yellow

Orange

Students

11

4

9

3

2

1

  • STEP 1 – Find the number of degrees that represents 1 student
    There are 30 students in total, so 360° = 30 students
    Divide both sides by 30, so 12° = 1 student
  • STEP 2 - Calculate the angle for each category by finding a fraction of 360°
    11 students out of 30 said red was their favourite colour, so this is 11 over 30 cross times 360 degree equals 132 degree
    4 students out of 30 said purple, so this is 4 over 30 cross times 360 degree equals 48 degree
    Repeat this for each category, they should sum to 360° in total

Colour

Red

Purple

Blue

Green

Yellow

Orange

Students

11

4

9

3

2

1

Angle

132°

48°

108°

36°

24°

12°

  • STEP 3 – Draw the pie chart, using a protractor to measure the angles
    Start by drawing a vertical line from the centre of the circle to the top ("12 o'clock")
    Then use your protractor to measure the first angle, and draw a line to this point
    Move your protractor to this line, and repeat for each category
    You should include a key or labels to show which slice represents which category

cie-igcse-pie-chart-protractor-part-1 cie-igcse-pie-chart-protractor-part-2

5B7-ZLel_cie-igcse-pie-chart-colours

 

How do I interpret a pie chart or find missing information?

  • It is easy to spot from a pie chart which category is the largest or smallest proportion, but you may be asked to do something more advanced like finding some missing information
  • Remember that all of the data is represented by 360°
  • You can use this to find either how many degrees each person/piece of data is represented by, or how many people/pieces of data 1 degree represents
  • For example if you are told that there is a slice measuring 30°  which represents 15 people
    •  30° = 15 people
    • 1° = 0.5 people (by dividing by 30)
  • 2° = 1 person (by dividing first statement by 15 or doubling the second statement)
    You can then use this information to help solve problems or find missing information

Exam Tip

  • If you are given a pie chart in an exam, it may not be to scale
  • If it is not to scale, do not try to use your protractor to measure it!
  • You will instead have to use the above methods to calculate the information you need

Worked example

The following pie chart is created to show the total value of items stocked in a sports shop for 4 different sports.

aqa-gcse-pie-chart-sports-stock

a)

Using the angle marked on the pie chart, and the fact that the shop stocks $12 000 worth of Golf items, find the total value of the shop’s stock across the 4 sports.

The angle marked on the diagram is 90°.

90 over 360 equals 1 fourth

So a quarter of the stock is for Golf.
We can multiply this by 4 to find the total value of the shop’s stock.

$ 12 space 000 cross times 4 equals $ 48 space 000

Total value is $48 000

b)

Given that the angle on the pie chart for Tennis is 72°, find the value of Tennis items the shop stocks.

The fraction of the value of the shop’s stock will be the same as the fraction of the circle for each category.

Therefore the value of tennis items will be

72 over 360 cross times $ 48 space 000 equals $ 9 space 600

Value of tennis items is $9 600

Number Toolkit
  • Mathematical Operations
  • Negative Numbers
  • Money Calculations
  • Number Operations
  • Related Calculations
  • Counting Principles
Prime Factors, HCF & LCM
  • Types of Number
  • Prime Factor Decomposition
  • HCF & LCM
Powers, Roots & Standard Form
  • Powers, Roots & Indices
  • Standard Form
Fractions
  • Basic Fractions
  • Operations with Fractions
Percentages
  • Basic Percentages
  • Working with Percentages
Simple & Compound Interest, Growth & Decay
  • Interest & Depreciation
  • Exponential Growth & Decay
Fractions, Decimals & Percentages
  • Converting between FDP
  • Converting between FDP
Rounding, Estimation & Bounds
  • Rounding & Estimation
  • Bounds
Surds
  • Simplifying Surds
  • Rationalising Denominators
Using a Calculator
  • Using a Calculator
Algebra Toolkit
  • Algebraic Notation & Vocabulary
  • Algebra Basics
Algebraic Roots & Indices
  • Algebraic Roots & Indices
Expanding Brackets
  • Expanding Single Brackets
  • Expanding Multiple Brackets
Factorising
  • Factorising
  • Factorising Quadratics
  • Quadratics Factorising Methods
Completing the Square
  • Completing the Square
Rearranging Formulae
  • Rearranging Formulae
Algebraic Proof
  • Algebraic Proof
Linear Equations
  • Solving Linear Equations
Solving Quadratic Equations
  • Solving Quadratic Equations
  • Quadratic Equation Methods
Simultaneous Equationsr
  • Simultaneous Equations
Iteration
  • Iteration
Forming & Solving Equations
  • Forming Equations
  • Equations & Problem Solving
Functions
  • Functions Toolkit
  • Composite & Inverse Functions
Coordinate Geometrys
  • Coordinates
  • Coordinate Geometry
Linear Graphs y = mx + c
  • Straight Line Graphs (y = mx + c)
  • Parallel & Perpendicular Lines
Graphs of Functions
  • Types of Graphs
  • Graphical Solutions
  • Trig Graphs
Equation of a Circle
  • Equation of a Circle
  • Equation of a Tangents
Estimating Gradients & Areas under Graphs
  • Finding Gradients of Tangents
  • Finding Areas under Graphs
Real-Life Graphs
  • Distance-Time & Speed-Time Graphs
  • Conversion Graphs
  • Rates of Change of Graphs
Solving Inequalities
  • Solving Linear Inequalities
  • Conversion Graphs
  • Solving Quadratic Inequalities
Graphing Inequalities
  • Graphing Inequalities
Transformations of Graphs
  • Reflections of Graphs
Sequences
  • Introduction to Sequences
  • Types of Sequences
  • Linear Sequences
  • Quadratic Sequences
Ratio Toolkit
  • Simple Ratio
  • Working with Proportion
Ratio Problem Solving
  • Ratios & FDP
  • Multiple Ratios
Direct & Inverse Proportions
  • Direct & Inverse Proportion
Standard & Compound Units
  • Time
  • Unit Conversions
  • Compound Measures
Exchange Rates & Best Buys
  • Exchange Rates & Best Buys
Geometry Toolkit
  • Symmetry
  • 2D & 3D Shapes
  • Plans & Elevations
Angles in Polygons & Parallel Lines
  • Basic Angle Properties
  • Angles in Polygons
  • Angles in Parallel Lines
Bearings, Scale Drawing, Constructions & Loci
  • Bearings
  • Scale & Maps
  • Constructing Triangles
  • Constructions & Loci
Circle Theorems
  • Angles at Centre & Semicircles
  • Chords & Tangents
  • Cyclic Quadrilaterals
  • Segment Theorems
  • Circle Theorem Proofs
Area & Perimeter
  • Area & Perimeter
  • Problem Solving with Areas
Circles, Arcs & Sectors
  • Area & Circumference of Circles
  • Arcs & Sectors
Volume & Surface Area
  • Volume
  • Surface Area
Congruence, Similarity & Geometrical Proof
  • Congruence
  • Similarity
  • Geometrical Proof
Area & Volume of Similar Shapes
  • Similar Area & Volumes
Right-Angled Triangles – Pythagoras & Trigonometry
  • Pythagoras Theorem
  • Right-Angled Trigonometry
  • Exact Trig Values
Sine, Cosine Rule & Area of Triangles
  • Sine & Cosine Rules
  • Area of a Triangle
  • Applications of Trigonomet
3D Pythagoras & Trigonometry
  • 3D Pythagoras & Trigonometry
Vectors
  • Introduction to Vectors
  • Working with Vectors
Transformations
  • Translations
  • Reflections
  • Rotations
  • Enlargements
  • Combination of Transformations
Probability Toolkit
  • Basic Probability
  • Relative & Expected Frequency
Simple Probability Diagrams
  • Two Way Tables
  • Frequency Trees
  • Set Notation & Venn Diagrams
Tree Diagrams
  • Tree Diagrams
Combined & Conditional Probability
  • Combined Probability
  • Conditional Probability
  • Combined Conditional Probabilities
Statistics Toolkit
  • Mean, Median & Mode
  • Averages from Tables
  • Range & Quartiles
  • Comparing Distributions
  • Population & Sampling
Statistical Diagrams
  • Bar Charts & Pictograms
  • Pie Charts
  • Time Series Graphs
  • Working with Statistical Diagrams
Histograms
  • Histograms
Cumulative Frequency & Box Plots
  • Cumulative Frequency Diagrams
  • Box Plots
Scatter Graphs & Correlation
  • Scatter Graphs