A pie chart divides one whole; sector angles must add to 360 degrees.
First identify the denominator. This chart describes the main journey mode of 20 surveyed residents. Each resident chooses one category, so walking, public transport and private transport are mutually exclusive parts of the same whole.
Calculate each share by dividing its frequency by the total. Walking accounts for 12/20 = 60%. Its sector angle is 0.6 x 360 = 216 degrees. Public transport is 30%, or 108 degrees; private transport is 10%, or 36 degrees. To draw the chart, use a protractor from a fixed starting radius, add the sectors in order and label them with a key.
Check that shares total 100% and angles total 360 degrees. Keep the sample size visible: 60% of 20 represents fewer people than 40% of 100. The sample alone does not establish the whole neighbourhood's travel pattern.
If people can select several modes, their responses overlap and may exceed 100%. Use a bar chart for that question, or define one main mode per journey before making a pie.
Step by step
Check the denominator
The categories must partition the same whole without overlap.
Calculate each angle
Frequency divided by total, multiplied by 360.
Draw and check
Use a protractor, label the key and total, and check all angles sum to 360.
Worked example: One calculation, two forms
Six of 20 residents use public transport as their main mode. The share is 6/20 = 30%; the angle is 6/20 x 360 = 108 degrees. The percentage and sector angle express the same proportion.
Watch out for this
A larger percentage always means a larger number of people.
Counts depend on the denominator. Compare sample sizes before converting shares into people.
Check your understanding
What angle represents 25% of a pie chart?
- 25 degrees.
- 90 degrees.
- 180 degrees.