GCSE Maths · Statistics · Foundation · Lesson 24.7

GCSE Maths: Pie charts (Foundation)

Part of the GCSE Maths statistics chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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24.7

Pie charts

Edexcel 1MA1: S2
Grade 2-5

A pie chart is a circle cut into sectors. The whole circle stands for all the data, and each sector’s angle shows its share. The whole circle is 360°, so a sector of 90° is a quarter of the data, and a sector of 180° is a half. Pie charts are good for showing proportions, but they do not show the actual numbers unless we are told the total.

The data 8, 12, 10, 6 has total 36, so each item is worth 360° ÷ 36 = 10°. The angles are 80°, 120°, 100° and 60°.

Drawing a pie chart. (1) Add the frequencies to find the total. (2) Divide 360° by the total to find the angle for one item. (3) Multiply each frequency by this angle. (4) Check that the angles add up to 360°. (5) Draw a circle, draw a radius, and use a protractor to measure each angle in turn. Label every sector.

Reading a pie chart. To find the frequency for a sector, write its angle as a fraction of 360° and find that fraction of the total: frequency = angle ÷ 360 × total. If you know the frequency of one sector but not the total, find how many degrees one item is worth: angle ÷ frequency, then divide 360 by it to find the total.

Comparing pie charts. A bigger sector in one pie chart does not necessarily mean more people, if the totals are different. Compare proportions (fractions or percentages), not sector sizes, unless the totals are given.

Key ideas

A full circle is 360°. Angle for one item = 360° ÷ total frequency.
Angle of a sector = frequency ÷ total × 360°.
Frequency of a sector = angle ÷ 360 × total.
The angles in a pie chart must add up to 360°.
Compare proportions, not raw sector sizes, when the totals differ.

Worked example 24.7.1

36 students were asked how they travel to school: walk 8, bus 12, car 10, cycle 6. Draw a pie chart to show this information.

Key words. A pie chart is a circle cut into sectors. The whole circle is 360° and stands for all the data. Each sector’s angle shows its share.

Method. Each category’s angle is its share of 360°: angle = frequency ÷ total frequency × 360°.

Add up the frequencies. The total is the whole pie, which is 360°.
8 + 12 + 10 + 6 = 36
Find the angle for one item. Divide the whole circle by the total frequency.
360° ÷ 36 = 10° for each item
Multiply each frequency by the angle for one item. A category with f items gets f lots of this angle.
Walk: 8 × 10° = 80°
Bus: 12 × 10° = 120°
Car: 10 × 10° = 100°
Cycle: 6 × 10° = 60°
Check that the angles make 360°. The angles of all the sectors must fill the circle.
80 + 120 + 100 + 60 = 360°
Draw the pie chart. Draw a circle with a compass and a radius. Then use a protractor to measure each angle in turn from the radius, going round the circle. Label each sector.

Check. Total = 360° = 360°. ✓

Watch out. Do not forget to check that the angles add up to 360°. If they do not, there is an arithmetic slip.

Worked example 24.7.2

120 students chose a favourite sport for a pie chart. The sector for football has angle 105°. How many students chose football?

Key words. A pie chart is a circle cut into sectors. The whole circle is 360° and stands for all the data. Each sector’s angle shows its share.

Method. A sector is a fraction of the whole pie. The fraction is angle ÷ 360°, and the same fraction of the total frequency belongs to the category.

Write the angle as a fraction of 360°. The whole circle is 360°, so the sector is angle over 360.
105360 = 724
Find one part of the total. The denominator is 24, so divide the total (120) into 24 equal parts.
120 ÷ 24 = 5
Multiply to find the sector. The sector is 7 of those parts.
7 × 5 = 35 students

Check. 1° stands for 120 ÷ 360 items, so 105° stands for 105 × 120 ÷ 360 = 35. ✓

Watch out. The pie shows a share of the total. Find the total first if it is not given.

Worked example 24.7.3

In a pie chart, 12 students chose tennis and the angle for tennis is 48°. How many students are represented by the whole pie chart?

Key words. A pie chart is a circle cut into sectors. The whole circle is 360° and stands for all the data. Each sector’s angle shows its share.

Method. If we know how many items match a sector, we can find how many items one degree stands for, and so find the total for the whole 360°.

Find what 1 item is worth in degrees. 12 students have an angle of 48°, so divide the angle by the frequency.
48° ÷ 12 = 4° for each item
Find how many items fill the whole circle. The whole pie is 360°.
360 ÷ 4 = 90
State the answer. The question asks for the total of the whole pie chart, not just the sector.
Total = 90

Check. 90 × 4° = 360°. ✓

Watch out. The total is for the whole pie, not for the sector you were told about.

Worked example 24.7.4

Pie chart A shows that 25% of a class of 40 walk to school (a sector of 90°). Pie chart B shows that 20% of a class of 100 walk to school (a sector of 72°). Lola says: “Class A has the bigger sector, so more students in Class A walk.” Is she right?

Key words. A pie chart is a circle cut into sectors. The whole circle is 360° and stands for all the data. Each sector’s angle shows its share.

Method. Work out the actual numbers using each pie chart’s total.

Class A. Use fraction of the total = angle ÷ 360, then multiply by the class size.
90360 = 14 and 14 of 40 = 10 students
Class B. Do the same.
72360 = 15 and 15 of 100 = 20 students
Compare. Class B has more students who walk, even though its sector is smaller.
20 > 10, so Lola is wrong about the numbers.

Check. 25% of 40 = 10 and 20% of 100 = 20. ✓

Watch out. Do not compare sector sizes without comparing the totals.

Watch out

The angles must add up to 360°, so always check. And when pie charts are for different totals, the same angle does not mean the same number of people.

Exercise 24G Pie charts

Calculator allowed

FWork out the angle for each sector in a pie chart for each set of data.

(a)Pets: dog 8, cat 6, fish 4, other 2 (20 pets)

(b)Lessons: maths 9, science 6, art 3, PE 6 (24 students)

(c)Fruit: apple 30, pear 20, banana 25, orange 15 (90 pieces)

Done

FThe table shows the colours of the cars in a car park.

Colour	Cars
Red	14
Blue	10
Silver	22
Black	14

Draw a pie chart to show this information.

Done

FTwenty-five children voted for their favourite playground game. The results are: tag 6, football 9, skipping 4, hopscotch 6. Work out the angle for each sector, giving your answers to 1 decimal place if necessary.

Done

FThe pie chart shows how 72 students spend their lunch break. The angle for “canteen” is 150°, for “playground” is 120° and for “library” is 90°. (a) What fraction of the students spend lunch in the canteen? (b) How many students spend lunch in the library? (c) How many students spend lunch in the playground?

(a)Fraction in the canteen

(b)Students in the library

(c)Students in the playground

Done

FEach pie chart has a sector with the given angle. Work out the number represented by that sector.

(a)Total 180 people; sector 60°

(b)Total 90 people; sector 140°

(c)Total 240 votes; sector 75°

(d)Total 54 cars; sector 100°

Done

PSWork out the total number of items represented by each whole pie chart.

(a)A sector of 30° represents 5 people.

(b)A sector of 80° represents 16 students.

(c)A sector of 45° represents 10 votes.

Done

PSA pie chart has sectors of 90°, 120°, 100° and one other sector. The total number of people is 72. (a) Work out the angle of the missing sector. (b) How many people does the missing sector represent?

(a)Missing angle

(b)People in the missing sector

Done

FIn a pie chart, a sector has angle 54°. What percentage of the data does it represent?

Done

RTwo pie charts show how students in Year 9 and in Year 11 travel to school. In Year 9 (120 students) the sector for “bus” is 60°. In Year 11 (180 students) the sector for “bus” is 50°. Which year group has more students travelling by bus?

Done

RDev says: “A pie chart shows a sector of 90° for football, so 90 people chose football.” Explain his mistake.

Done

PSThe frequency table shows the drinks chosen by 25 people. Work out the angle for each drink, and show that the angles add up to 360°.

Drink	Frequency
Tea	7
Coffee	11
Juice	5
Water	2

Done

PSA pie chart shows the favourite ice cream flavours of 60 people. The angles are chocolate 150°, vanilla 90°, strawberry 72° and mint 48°.
(a) How many people chose vanilla? (b) What percentage chose strawberry?

(a)People who chose vanilla

(b)Percentage who chose strawberry

Done

RIn two pie charts the sector for “cycling” is 90° in both. The first pie chart shows 80 students and the second shows 120 students. How many more students cycle in the second pie chart than in the first?

Done