Pie charts, which represent quantities as sectors of a circle, can be used to illustrate data. They are particularly effective if there is only a small number of items to illustrate. In total a complete circle, i.e. 360°, must always be used.
Worked Examples
Tracey uses her pocket money of £18 per month in the following way.
| Books | £4 |
| Sweets | £3 |
| Sport | £6 |
| Transport | £4 |
| Savings | £1 |
Draw a pie chart to show how Tracey uses her pocket money.
Tracey has a total of £18.
= 20°
So 20° should be used for each £1. The angles needed are given in this list.
| Books | 4 × 20° = 80° |
| Sweets | 3 × 20° = 60° |
| Sport | 6 × 20° = 120° |
| Transport | 4 × 20° = 80° |
| Savings | 1 × 20° = 20° |
Alternatively, you could calculate each angle by taking the appropriate fraction of 360°.
For example, for Books, we have
× 360° = 80°
and for Sweets,
× 360° = 60°, etc.
The pie chart can now be drawn.
The diagram below, on the left, shows the first section for 'Books'.
The completed pie chart is on the right.
The pie chart was constructed after asking 72 students how they travel to school.
How many of these students travel to school by:
There are 72 students so
= 5° per student
car,
Show meThe angle for travelling by car is 40°.
= 8
So 8 students travel by car.
bus,
Show meThe angle for travelling by bus is 20°.
= 4
So 4 students travel by bus.
taxi?
Show meThe angle for travelling by taxi is 110°.
= 22
So 22 students travel by taxi.
What percentage walk to school?
Show meThe number who walk to school is given by
= 38
so the percentage who walk is
× 100 ≈ 52.8%
Note
Alternatively, you could just use the angles in the pie chart to give
× 100 ≈ 52.8%
The pie chart below, not drawn to scale, shows the Saturday morning activities of a group of 120 children.
The sector for soccer is represented by an angle of 150°. Determine the number of children who play soccer on Saturday mornings.
Show me| Number playing soccer | = × 120 |
| = 50 children |
Given that 46 children swim on Saturday mornings, calculate the value of x.
Show me| Angle for swimming | = × 360° |
| = 138° |
Determine the probability that a child chosen at random, dances on Saturday mornings.
Show me| Number dancing | = 120 − (50 + 46) |
| = 120 − 96 | |
| = 24 | |
| So probability of dancing | = = |
(Probability is covered in detail in another units.)
Exercises
