Pie charts
A pie chart cuts a circle into slices. The more a slice stands for, the bigger its angle.
A pie of 40 students
A class of 40 students got grades A, B, C, D and E: 12, 10, 8, 6 and 4 students. We will show this on a pie chart.
Grade A has 3 times as many students as grade E (12 and 4). How will the angle of the A slice compare with the E slice?
What this lesson covers
The idea
A pie chart shows the different proportions of a whole as slices of a circle, the angle of each slice being proportional to the quantity it represents.
A pie of 40 students
A class of 40 students got grades A, B, C, D and E: 12, 10, 8, 6 and 4 students. We will show this on a pie chart.
Grade A has 3 times as many students as grade E (12 and 4). How will the angle of the A slice compare with the E slice?
- 3 times as big
- The same angle
- 8° bigger, because 12 − 4 = 8
Build the pie
The circle has one wedge for every student, 40 wedges. Tap each grade to give it its wedges, starting at the black radius and turning anticlockwise. Look at the angle of every slice.
Angle is proportional to the quantity
A pie chart shows the different proportions of a whole as slices of a circle, the angle of each slice being proportional to the quantity it represents.
One student is one wedge: 360° ÷ 40 = 9°. Grade A has 12 × 9° = 108° and grade E has 4 × 9° = 36°.
The angles are 3 times as big because the students are 3 times as many: 108° = 3 × 36°. Twice the quantity, twice the angle.
All the slices together make the whole circle: 108° + 90° + 72° + 54° + 36° = 360°
Notes
A pie chart shows the different proportions of a whole as slices of a circle, the angle of each slice being proportional to the quantity it represents.
Check yourself
A pie chart shows the 36 students of a class. One slice measures 90°. How many students does that slice stand for?
Answer: 9 students
360° ÷ 36 = 10°, so one student is 10°. The slice has 90° ÷ 10° = 9 students. (90° is a quarter of the circle, and a quarter of 36 is 9.)
In a pie chart, slice Q is 40°. Slice P stands for twice as many as Q. How many degrees is slice P?
Answer: 80 °
The angle is proportional to the quantity. P stands for twice as many as Q, so its angle is 2 × 40° = 80°.
The pie chart shows what 24 students like to play. How many students chose football?
Answer: 6 students
The football slice is a right angle, a quarter of the circle. A quarter of 24 students is 6. (Each student is 360° ÷ 24 = 15°, and 90° ÷ 15° = 6.)
Why do the angles of all the slices of a pie chart add up to 360°?
- Because every slice is 90°.. Slices have different angles. Each is proportional to its quantity.
- Because the slices together fill the whole circle, which stands for the whole data. — correct. Yes! The circle is the whole, so all the quantities together fill all 360°.
- Because there are always 360 students.. The number of students can be anything. The whole circle, 360°, stands for all of them, whatever the number is.