Pie Charts (Edexcel GCSE Statistics)

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

• 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

  • 4 students out of 30 said purple,

    • so this is

  • Repeat this for each category, they should sum to 360° in total

• 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

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

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

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

  • 

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

    • is the total frequency of data set 1

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

    • is the total frequency of data set 2

  • It can be rearranged as  

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

  • Or as  

    • This can be used to find 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

    • So we want the areas to give  

    • That's the same as  

    • Cancel the 's to get  

  • To get the '' version

    • multiply both sides by to get   

    • then take square roots:   

  • To get the '' version

    • multiply both sides by to get   

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