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Statistical Diagrams

Statistics

Drawing one

  • A pie chart divides a circle into sectors, one for each category, showing the proportions rather than the actual frequencies
  • Each sector angle is that category's share of the whole turn
    • Angle = (frequency ÷ total frequency) × 360°
  • Work out every angle, then check they add to 360° before drawing anything
  • Draw with a protractor from a radius already drawn, measuring each angle from the previous boundary
  • Label every sector or provide a key
A pie chart of students' favourite colour with each sector angle written on it: red 132 degrees, purple 48, blue 108, green 36, yellow 24 and orange 12, which add to 360, alongside a key naming each colour
Source: Pie charts by Save My Exams

Reading one

  • Going the other way, frequency = (angle ÷ 360°) × total frequency
  • A sector's angle alone cannot give a frequency without the total, which is why two pie charts of different sizes cannot be compared directly
Exam tip

Show the line "frequency ÷ total × 360" for each sector. That calculation is what carries the marks, not the drawing, and a sector whose angle is right but drawn a degree or two out is still credited.

Worked example

Calculating pie chart angles

Forty people are asked their favourite drink. Tea is chosen by 14, coffee by 12, juice by 9 and water by 5. Work out the angle of each sector.

Solution:

  • Each angle is the category's share of 360°
  • Tea: 14 ÷ 40 × 360 = 126°
  • Coffee: 12 ÷ 40 × 360 = 108°
  • Juice: 9 ÷ 40 × 360 = 81°
  • Water: 5 ÷ 40 × 360 = 45°
  • Check: 126 + 108 + 81 + 45 = 360