Pie Charts

Worked example

1. 1

   $\text{Bus}=108^{\circ }$ — Measure the bus sector with a protractor: centre on the middle of the circle, 0 on one edge, read where the other edge crosses. It is 108°.

2. 2

   $\frac{108}{360}$ — Put the sector's angle over the whole circle. This is the fraction of people who took the bus.

3. 3

   $\frac{108÷36}{360÷36}=\frac{3}{10}$ — Simplify. 36 is the biggest number that goes into both 108 and 360, so divide top and bottom by 36.

4. 4

   $\frac{3}{10}\times 100=30\%$ — For a percentage, times the fraction by 100. So 30% took the bus.

Worked example

1. 1

   $360÷60=6^{\circ }$ — Share the 360° equally between the 60 people. Each person gets 6°. This is the formula done in a handy order.

2. 2

   $\text{Apple: }21\times 6=126^{\circ }$ — 21 people chose apple, and each one is worth 6°, so times 21 by 6.

3. 3

   $\text{Banana: }18\times 6=108^{\circ }$ — Same move for banana: 18 people at 6° each.

4. 4

   $\text{Pear: }12\times 6=72^{\circ }$ — Pear: 12 people at 6° each.

5. 5

   $\text{Grape: }9\times 6=54^{\circ }$ — Grape: 9 people at 6° each.

6. 6

   $126+108+72+54=360$ — Check: the angles must make a full turn. If they do not, one of them is wrong.

Worked example

1. 1

   $\text{Start line: centre to edge}$ — Every sector needs an edge to measure from. Draw a line from the centre straight up to the circle, unless the exam has drawn one.

2. 2

   $\text{Apple}=126^{\circ }$ — Put the protractor's centre on the circle's centre and its 0 on the start line. Mark 126° and join the mark to the centre.

3. 3

   $\text{Banana}=108^{\circ }$ — Now put 0 on the apple line you just drew, not the start line. Mark 108° and join it to the centre.

4. 4

   $\text{Pear}=72^{\circ }$ — Same again, measuring from the banana line.

5. 5

   $\text{Grape}=360-126-108-72=54^{\circ }$ — Grape is the gap that is left. Measure it: if it is not 54°, one of your earlier sectors is off.

6. 6

   $\text{Label each sector}$ — Write apple, banana, pear and grape in their slices, so the reader knows which is which.

Worked example

1. 1

   $150^{\circ }=45\text{ people}$ — Start from the sector you know: 150° stands for 45 people.

2. 2

   $1^{\circ }=45÷150=0.3$ — Divide to find what one degree stands for: 0.3 of a person. Then any angle can be turned into people.

3. 3

   $\text{Walking}=80\times 0.3=24$ — Walking is 80°, and each degree is 0.3 people, so 80 × 0.3 = 24 people.

4. 4

   $\text{Total}=360\times 0.3=108$ — If asked for everyone, use the whole circle: 360 × 0.3 = 108 people.

Worked example

1. 1

   $\frac{90}{360}=\frac{1}{4}$ — A 90° sector is a quarter of the circle, so it is a quarter of the people.

2. 2

   $\frac{1}{4}\times 108=27$ — A quarter of the 108 people is 27 people.

Worked example

1. 1

   $140-100=40^{\circ }$ — Find the gap between the car and bus sectors: 40°.

2. 2

   $40^{\circ }=30\text{ people}$ — The extra 40° is the extra 30 people, so these two match.

3. 3

   $1^{\circ }=30÷40=0.75$ — Divide to find what one degree stands for: 0.75 of a person.

4. 4

   $\text{Walk}=360-140-100=120^{\circ }$ — Walk is the rest of the circle, because the angles add up to 360°.

5. 5

   $120\times 0.75=90\text{ people}$ — Turn walk's angle into people: 120 × 0.75 = 90.

Worked example

1. 1

   $96÷8=12^{\circ }$ — Tea is the only row with both numbers. 96° for 8 people means each person gets 12°.

2. 2

   $\text{Coffee: }120÷12=10$ — To turn an angle into people, divide by 12°. So 10 people chose coffee.

3. 3

   $\text{Juice: }5\times 12=60^{\circ }$ — To turn people into an angle, times by 12°.

4. 4

   $96+120+60=276^{\circ }$ — Add up the angles you know so far.

5. 5

   $\text{Water: }360-276=84^{\circ }$ — The angles add up to 360°, so water gets what is left.

6. 6

   $84÷12=7\text{ people}$ — Turn water's angle into people by dividing by 12°.

7. 7

   $8+10+5+7=30$ — Check: the people add up to the 30 who were asked.

Worked example

1. 1

   $\text{Elephants}:\text{giraffes}=120:60$ — Every animal gets the same number of degrees, so the angles are in the same ratio as the numbers. Write the two angles.

2. 2

   $=2:1$ — Divide both by 60, the biggest number that goes into both. This is the simplest form.

Worked example

1. 1

   $\text{A: }\frac{90}{360}\times 40=10$ — 90° is a quarter of the circle, and a quarter of Class A's 40 students is 10.

2. 2

   $\text{B: }\frac{90}{360}\times 200=50$ — Same angle, but a quarter of Class B's 200 students is 50.

3. 3

   $10\ne 50$ — Same angle, different numbers. An angle shows a share of the group, not how many.