Pie Charts (Edexcel GCSE Statistics)

Revision Note

Pie Charts

What is a pie chart?

  • A pie chart is a circle which is divided into slices (sectors) to show proportions

  • They show the relative size of categories of data compared to each other

    • rather than their actual size or number

      • e.g. looking at the proportions of men and women working for a company, we might be more interested in the relative sizes of the groups than in the actual numbers of men and women

  • There are 360° in a circle

    • 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 the next category

    • Continue until the slices for all the categories are drawn

    • You should include a key or labels to show which slice represents which category

Protractor measuring 132 degrees
Protractor measuring 48 degree angle
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 the information you are given to find

    • how many degrees each person/piece of data is represented by

    • 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 (divide by 30)

      • 2° = 1 person (divide the first statement by 15, or double the second statement)

    • You can then use this information to help solve problems or find missing information

Examiner Tips and Tricks

  • A pie chart given in an exam may not be to scale

    • If it is not to scale, do not try to use your protractor to measure it!

    • Instead use the methods described in this revision note 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.

cie-igcse-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
That means we can multiply the value of the golf stock by 4 to find the total value of the shop’s stock

12000 cross times 4 equals 48000

Total value is $48 000

(b) Given that the angle on the pie chart for Tennis is 72°, find the value of the Tennis items that 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

48000 cross times 72 over 360 equals 9600

Value of tennis items is $9 600

Comparative Pie Charts

How are comparative pie charts different from regular pie charts?

  • For two data sets of different sizes (different total frequencies), drawing two pie charts that are the same size can be misleading

    • It makes it 'look like' the two sets are the same size

    • A sector ('slice') in one pie chart can be the same size as a sector in the other one

      • even though the number of things represented can be very different

  • With comparative pie charts, the areas of the two pie charts are in the same ratio as the total frequencies of the two data sets

    • e.g. if one pie chart represents data for 500 people and the other one represents data for 1000 people

    • then the area of the second chart will be twice as big as the area of the first one

      • because 500 colon 1000 space equals space 1 colon 2

  • The relationship between the radiuses of two pie charts and the total frequencies of their data sets can be given by the formula

    • F subscript 2 over F subscript 1 equals r subscript 2 squared over r subscript 1 squared

      • r subscript 1 is the radius of the pie chart for data set 1

      • F subscript 1 is the total frequency of data set 1

      • r subscript 2 is the radius of the pie chart for data set 2

      • F subscript 2 is the total frequency of data set 2

    • It can be rearranged as  r subscript 2 equals r subscript 1 cross times square root of F subscript 2 over F subscript 1 end root

      • This can be used to find r subscript 2 if you know the other three values

    • Or as  F subscript 2 equals F subscript 1 cross times r subscript 2 squared over r subscript 1 squared

      • This can be used to find F subscript 2 if you know the other three values

  • The formula is not in the formula booklet so you need to remember it

    • It might help if you understand where it comes from

      • Remember that the area of a circle is pi r squared

      • So we want the areas to give  F subscript 2 colon F subscript 1 equals pi r subscript 2 squared colon pi r subscript 1 squared

      • That's the same as  F subscript 2 over F subscript 1 equals fraction numerator pi r subscript 2 squared over denominator pi r subscript 1 squared end fraction

      • Cancel the pi's to get  F subscript 2 over F subscript 1 equals r subscript 2 squared over r subscript 1 squared

    • To get the 'r subscript 2 equals' version

      • multiply both sides by r subscript 1 squared to get   r subscript 2 squared equals r subscript 1 squared cross times F subscript 2 over F subscript 1

      • then take square roots:   r subscript 2 equals square root of r subscript 1 squared cross times F subscript 2 over F subscript 1 end root equals r subscript 1 cross times square root of F subscript 2 over F subscript 1 end root

    • To get the 'F subscript 2 equals' version

      • multiply both sides by F subscript 1 to get   F subscript 2 equals F subscript 1 cross times r subscript 2 squared over r subscript 1 squared

How do I compare two data sets represented by comparative pie charts?

  • When comparing two data sets represented by comparative pie charts:

    • To compare frequencies compare areas

      • This is true for the total frequencies

      • It is also true for the frequencies of individual sectors

    • To compare proportions compare the angles of the sectors

  • If a question asks you about frequencies of individual sectors

    • it is may be easier to find the total frequencies of the pie charts first

    • See the Worked Example

Examiner Tips and Tricks

  • If the question tells you that comparative pie charts are "drawn accurately", then you can find

    • their radiuses by measuring with your ruler

    • the angles of sectors by measuring with your protractor

Worked Example

In 2022, a cruise line started offering combined '18-30, 45-55 and 70+' cruises.

The comparative pie charts show information about the numbers of people from each age group that went on these cruises in 2022 and in 2023.

Comparative pie charts for the two data sets referred to in the question

The radius of the pie chart for 2023 is smaller than the radius of the pie chart for 2022.

(a) Explain what can be deduced from this information.

A smaller radius means a smaller area
And with comparative pie charts a smaller area means a smaller total frequency

Fewer people went on the cruises in 2023

1250 people who were 70+ years old went on the cruises in 2022.

The radius of the 2022 pie chart is 5 cm, and the radius of the 2023 pie chart is 3 cm.

(b) Work out the number of people who were 70+ years old that went on the cruises in 2023.

Work out the total number of people who went on cruises in 2022
90 over 360 of the 2022 circle is taken up by the '70+' sector
That corresponds to 1250 people, so

table row cell 90 over 360 cross times 2022 space total end cell equals 1250 row blank blank blank row cell 1 fourth cross times 2022 space total end cell equals 1250 end table

Divide both sides by 1 fourth

2022 space total equals 1250 divided by 1 fourth equals 1250 cross times 4 equals 5000

Use F subscript 2 over F subscript 1 equals r subscript 2 squared over r subscript 1 squared to find the total number of people for 2023
F subscript 1 equals 5000,  r subscript 1 equals 5  and  r subscript 2 equals 3
F subscript 2 will then be the total frequency for 2023

fraction numerator 2023 space total over denominator 5000 end fraction equals 3 squared over 5 squared

Multiply both sides by 5000

2023 space total equals 5000 cross times 3 squared over 5 squared equals 5000 cross times 9 over 25 equals 1800

Now work out the number of people 70+ years old who went on cruises in 2023
120 over 360 of the 2023 circle is taken up by the '70+' sector, so

120 over 360 cross times 1800 equals 1 third cross times 1800 equals 600

 
600 people who were 70+ years old went on the cruises in 2023

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Roger B

Author: Roger B

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

Dan Finlay

Author: Dan Finlay

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Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.