Pie Charts (SQA National 5 Applications of Mathematics): Revision Note

Pie charts

What is a pie chart?

• A pie chart is a circle divided into sectors which is used to present data

• The sectors represent different categories

  • They show the relative proportions of the categories

  • They do not show the actual frequencies of each category

How do I find the angles for a pie chart?

• STEP 1
  Add the frequencies together

  • e.g. 11 + 4 + 9 + 3 + 2 + 1 = 30

• STEP 2
  Write each frequency as a fraction out of the total frequency

  • e.g. Red =

• STEP 3
  Find each angle by finding the fraction of 360°

  • With a calculator, just multiply

    • e.g.

  • Without a calculator, divide 360° by the total frequency and multiply by the frequency of that item

    • e.g. 360° ÷ 30 = 12° and 12° × 11 = 132°

How do I draw a pie chart?

• Draw a vertical line from the circle's centre to the top, then use a protractor to mark off the first angle

  • Draw a line from the centre to this first mark

    • Then, from this line, mark off the next angle (and so on)

      
      

How do I find frequencies using a pie chart and the total frequency?

• STEP 1
  Write each angle as a fraction out of the 360

  • e.g. for an angle of 84°, write

• STEP 2

• Find each frequency by finding the fraction of the total frequency

  • With a calculator, just multiply

    • e.g. for a total frequency of 180,

  • Without a calculator, divide the total frequency by 360° and multiply by the angle

    • e.g. 180 ÷ 360 = 0.5 and 0.5 × 84 = 42

How can I use ratio and proportion with pie charts?

• You can find missing angles and frequencies using the following facts

  • angles are proportional to the frequencies of each category

  • 360° represents the total frequency 

• You can work out

  • what frequency is represented by 1°

  • what angle is represented by 1 unit of frequency

• For example, if a sector of 30° represents 15 people, then

  • 1° = 0.5 people (dividing by 30)

  • 2° = 1 person (multiplying by 2)

• These relationships can then be scaled up or down accordingly

  • If 1° = 0.5 people

    • then 360° = 180 people (multiplying by 360)