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Daily Maths

Pie charts

Pie Charts Core + Extended 8 min read

On this page
  1. In this note
  2. Formula bank
  3. Drawing a pie chart
  4. Reading a pie chart
  5. Ways they test it
  6. Mistakes to avoid
  7. Summary
  8. Practice
  9. Can I do this?
  10. Quiz

In this note

Syllabus 9.3: pie charts
  • 9.3Work out sector angles from a table and draw a pie chart.
  • 9.3Read a pie chart: a frequency from an angle, the total from one sector, a missing angle.
  • 9.3Compare two pie charts fairly.

Before you start: ratio and proportion and angles round a point (360°).

Formula bank

Degrees per itemLearn it\(\dfrac{360}{\text{total}}\)the one number that unlocks every question.Use it when drawing or reading a pie chart.
Sector angleLearn it\(\dfrac{\text{frequency}}{\text{total}}\times360°\)Use it when you know the frequency.
FrequencyLearn it\(\dfrac{\text{angle}}{360}\times\text{total}\)Use it when you know the angle.
Angles round the centreLearn itall sector angles add up to 360°Use it when missing angles; checking your angles.

Drawing a pie chart

The whole circle (360°) stands for everyone in the survey, so each sector is the same fraction of 360° as its group is of the total. In a survey of 40 people each person gets \(360\div40=9°\).

Favourite sport of 40 studentsFootball126°Cricket99°Hockey54°Tennis81°
40 students: 9° per student.
SportFrequencyAngle
Football1414 × 9 = 126°
Cricket1111 × 9 = 99°
Hockey66 × 9 = 54°
Tennis99 × 9 = 81°
Total40360°

General methodHow to draw any pie chart

  1. Add up the frequencies; work out 360 ÷ total (degrees per item).
  2. Multiply each frequency by it. Check the angles add to 360°.
  3. Draw a circle and a radius. Measure the first angle with a protractor; carry on from each new line.
  4. Label every sector with its category.

Try it yourself

1
A survey of 24 people. How many degrees per person?
Show answer

Answer 15°

2
Of 30 people, 12 chose red. Sector angle?
Show answer

Answer 144°

3
A quarter of the people chose X. Sector angle?
Show answer

Answer 90°

Reading a pie chart

General methodHow to read any pie chart

  1. Angle → frequency: angle ÷ 360 × total (or angle ÷ degrees per item).
  2. One sector gives the total: find people per degree (or degrees per person), then × 360.
  3. Missing angle: all angles add to 360, so make an equation.
  4. Comparing two charts with different totals: work out the actual NUMBERS.

Example A sector of 48° stands for 16 people. How many are in the survey?

Degrees per person, then 360 ÷ it.

  1. 1 person = 48 ÷ 16 = 3°
  2. \(360\div3=120\)

Answer 120 people

Try it yourself

1
A pie chart shows 200 cars; the 'red' sector is 45°. How many red cars?
Show answer

Answer 25

2
A 100° sector stands for 10 people. Total?
Show answer

Answer 36

3
Sectors 90°, 120°, x° and 2x°. Find x.
Show answer

Answer 50

Ways they test it

Type 1 Complete the table and draw

"Complete the pie chart" from a frequency table (3-4 marks)

Spot it a table of frequencies.

  1. 360 ÷ total.
  2. Each angle; check 360.
  3. Draw (±2°), label.

For example Bus 21, Car 15, Walk 18, Cycle 6 (60 students)

  1. 6° each
  2. 126°, 90°, 108°, 36°

Answer the four angles, then draw

Type 2 Angle to frequency

"The pie chart shows 90 people. How many chose each fruit?"

Spot it a drawn chart and a total.

  1. Degrees per person.
  2. Each angle ÷ it.

Type 3 Total from one sector

"Rice is 75° and represents 30 people. How many were asked?"

Spot it one sector's number given.

  1. People per degree.
  2. × 360.

For example 75° ↔ 30

  1. \(30\div75=0.4\)
  2. \(0.4\times360=144\)

Answer 144 people

Type 4 Angles with algebra

"Sectors x°, 2x°, (3x + 30)° and 90°..."

Spot it letters in the angles.

  1. Add to 360, solve.
  2. Then use the angle.

Type 5 Compare two charts

"Ali says more walk to School A because its sector is bigger. Is he right?" (2 marks)

Spot it two pie charts, different totals.

  1. Work out both numbers.
  2. Conclude with both figures.

For example A: 600 students, 90°; B: 900 students, 72°

  1. A: \(\tfrac{90}{360}\times600=150\)
  2. B: \(\tfrac{72}{360}\times900=180\)

Answer No: B has more (180)

Mistakes to avoid

  • ✗ Angle = frequency✓ angle = frequency × 360 ÷ totalOnly true if the total is 360.
  • ✗ Bigger angle = more people✓ compare actual numbersThe totals may differ.
  • ✗ Sectors labelled only with angles✓ label with the categoryLabels earn the mark.
  • ✗ Angles adding to 350° drawn anyway✓ check they add to 360°A slip somewhere.

Summary

  • Degrees per item = 360 ÷ total.
  • Angle ↔ frequency through that one number.
  • Angles add to 360°: missing angles and checking.
  • Sector size shows a proportion, not a number.

If you see …

  • a frequency table360 ÷ total, then × each.
  • one sector's numberpeople per degree × 360.
  • two charts to comparework out actual numbers.

Practice

Practice: easy, medium, hard

Easy

1
60 students: Bus 21, Car 15, Walk 18, Cycle 6. Angle for Bus?
Show working
  1. 360 ÷ 60 = 6
  2. \(21\times6=126\)

Answer 126°

2
A pie chart of 90 people has an 'apple' sector of 140°. How many chose apple?
Show working
  1. \(140\div4=35\)

Answer 35

3
Sectors x, x, 2x and 120°. Find x.
Show working
  1. \(4x=240\)

Answer 60

Medium

1
Rice is 75° and represents 30 people. How many were asked?
Guide me

What is it asking? the total

What do we know? 75° ↔ 30

Plan people per degree × 360

Show working
  1. \(30\div75=0.4\)
  2. \(0.4\times360=144\)

Answer 144

2
In a pie chart of 160 votes, Amir's sector is 117°. How many votes did he get?
Guide me

What is it asking? Amir's votes

What do we know? 117° out of 360

Plan \(\tfrac{117}{360}\times160\)

Show working
  1. \(\tfrac{117}{360}\times160=52\)

Answer 52

3
Bina got 30% of the votes. Angle of her sector?
Guide me

What is it asking? the angle

What do we know? 30%

Plan 30% of 360

Show working
  1. \(0.3\times360\)

Answer 108°

Hard

1
Sectors x°, 2x°, (3x + 30)° and 90° show 216 people. How many people does the largest sector represent?
Guide me

What is it asking? people in the largest sector

What do we know? angles add to 360

Plan solve for x, find the largest angle, then people

Show working
  1. \(6x+120=360\Rightarrow x=40\)
  2. largest: 150°
  3. \(\tfrac{150}{360}\times216=90\)

Answer 90

PartAnswer / workingMarksGuidance
\(6x+120=360\)M1
\(x=40\)A1
150° usedM1
90A1
Total: 4 marks
2
Chart P: 1000 people, sector 36°. Chart Q: 500 people, sector 54°. How many more people in P's sector than Q's?
Guide me

What is it asking? the difference in people

What do we know? different totals

Plan work out both numbers

Show working
  1. P: \(\tfrac{36}{360}\times1000=100\)
  2. Q: \(\tfrac{54}{360}\times500=75\)

Answer 25

PartAnswer / workingMarksGuidance
100 and 75M1
25A1
Total: 2 marks
3
Sectors 40°, 75°, y° and 4y°. Find the largest sector.
Guide me

What is it asking? the largest angle

What do we know? four angles, total 360

Plan solve 115 + 5y = 360

Show working
  1. \(5y=245\Rightarrow y=49\)
  2. \(4y=196\)

Answer 196°

PartAnswer / workingMarksGuidance
\(40+75+5y=360\)M1
49A1
196A1
Total: 3 marks

Can I do this?

Anything unticked: revise that section first. All ticked: take the quiz.

Quiz

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