Pie Charts

The modal category is the one with the greatest frequency.

Use the angle mark to identify the share of the full circle.

Divide the sector angle by the angle of a full circle.

Find the fraction choosing art, then multiply by 360.

Each person represents 360 divided by the total number of people.

Find what fraction of 360 degrees the sector represents.

1. \frac{45}{360}=\frac18, so cyclists =80\div8=10.

Subtract the two known angles from a full turn.

1. Known angles =180+72=252°.
2. So x=360-252=108°.

Use the same percentage of the full circle.

1. Angle =\frac{20}{100}\times360=72°.

A 180-degree sector is half the circle.

1. Reading count =46\div2=23 pupils.

Compare the two equal frequencies, and check whether a reader can identify each category.

1. The sectors are not labelled with their pet categories, so the reader cannot identify them.
2. Dogs and rabbits both have frequency 18. Their angles should both be \frac{18}{48}\times360=135°, but the drawn sectors have three different sizes.
3. The cat angle should be \frac{12}{48}\times360=90°. Frequencies must be scaled to a full turn; they are not angles.

Use the table total to convert each remaining frequency into an angle.

Part (a)

1. Tennis represents \frac{12}{45} of the pupils.
2. Tennis angle =\frac{12}{45}\times360=96°.

Part (b)

1. Netball angle =\frac{15}{45}\times360=120°.
2. The check is 144+96+120=360°. On paper, measure each angle at the centre, beginning at the previous boundary, and label the sectors with their sports.
3. The completed chart uses these angles and identifies every category.

Apply the fraction of the full circle to the total.

1. Tea count =\frac{75}{360}\times72=15 people.

A sector angle describes a share of that chart’s whole group.

1. The bus angle is 120° at B and 100° at A, so B has the larger proportion.
2. The charts may represent different group sizes. We cannot tell which school has more bus users without knowing both totals.

Find the fraction represented by 240 degrees and work back to the whole.

1. \frac{240}{360}=\frac23. If two thirds is 20, one third is 20\div2=10.
2. The whole is 10\times3=30 pupils.

Take the sector’s fraction of the whole budget.

1. Equipment cost =\frac{54}{360}\times800=£120.

Use the angle marks to find the art angle, then compare the art and drama shares.

1. Drama has a right-angle mark, so its angle is 90°.
2. Art angle =360-90-110=160°.
3. 90° represents 18 members, so the number choosing art is 18\times\frac{160}{90}=32.
4. Alternatively, the club has 18\times4=72 members, and \frac{160}{360}\times72=32 chose art.

Calculate the two counts before comparing them.

1. A: \frac{108}{360}\times40=12 walkers.
2. B: \frac{90}{360}\times60=15 walkers.
3. Difference =15-12=3 more walkers in B, despite B’s smaller angle.

Use the wooden sector to find the total number of buttons. The question about holes uses that same total.

1. The wooden sector is a right angle, so wooden buttons make up one quarter of all the buttons.
2. Total buttons =18\times4=72.
3. Probability of four holes =\frac{20}{72}=\frac5{18}. The denominator is the number of buttons, not 360 degrees.

Update both the bus count and the overall count.

1. Original bus users =\frac{144}{360}\times50=20.
2. New bus count =20+10=30. New total =50+10=60.
3. New angle =\frac{30}{60}\times360=180°.

Recover each cycling count, then use the combined group size.

1. First group: \frac{120}{360}\times30=10 cyclists.
2. Second group: \frac{144}{360}\times50=20 cyclists.
3. Combined cyclists =10+20=30. Total people =30+50=80.
4. Percentage =\frac{30}{80}\times100=37.5\%.