For each statement about pie charts, write down whether it is True or False.
(i)In a pie chart, the angles of all the sectors must add up to 360 degrees.(1)
(ii)A pie chart can only be used when there are exactly four categories of data.(1)
(Total for Question 1 is 2 marks)
2
A number of pupils were asked to name their favourite school sport. The pie chart shows the results, with the number of pupils choosing each sport written on each sector.
(a)Write down the sport that was most popular.(1)
(b)Work out the total number of pupils who took part in the survey.(2)
(Total for Question 2 is 3 marks)
3
50 people were asked to name their favourite ice cream flavour. The pie chart shows the results, with the percentage of people choosing each flavour written on each sector.
(a)Write down the least popular flavour.(1)
(b)Work out the number of people who chose mint as their favourite flavour.(2)
(Total for Question 3 is 3 marks)
4
20 children were asked to name their favourite colour. The pie chart shows the results, with the angle of each sector written on the chart.
(a)Write down the most popular colour.(1)
(b)Write down the colour chosen by exactly a quarter of the children.(1)
(c)Write down, as a fraction in its simplest form, the proportion of children whose favourite colour was green.(1)
(Total for Question 4 is 3 marks)
5
30 people were asked to choose their favourite drink from a list. The table shows the results.
Drink
Tea
Coffee
Juice
Water
Frequency
8
4
6
12
(a)Write down, as a fraction in its simplest form, the proportion of people who chose coffee.(2)
(b)Write down, as a fraction in its simplest form, the proportion of people who chose water.(1)
(Total for Question 5 is 3 marks)
6
60 people were asked how they usually travel to work. The table shows the results.
Method
Car
Bus
Walk
Cycle
Frequency
27
15
12
6
The results are to be shown in a pie chart.
(a)Calculate the angle of the sector that represents Bus.(2)
(b)Explain why the angles for all four methods of travel must add up to 360 degrees.(1)
(Total for Question 6 is 3 marks)
7
70 people were asked how they get to work. 23 of them said they travel by car.
Work out the angle that should be used to represent 'car' on a pie chart. Give your answer correct to the nearest degree.
(Total for Question 7 is 2 marks)
8
A pie chart is going to show the results of a pet survey. A student has calculated these angles.
Pet
Dog
Cat
Fish
Other
Angle
130 deg
110 deg
90 deg
40 deg
Explain why the student must have made an error.
(Total for Question 8 is 2 marks)
9
90 students were asked to name their favourite film genre. The table shows the results.
Genre
Action
Comedy
Horror
Romance
Frequency
30
20
15
25
Calculate the angle needed to represent each genre in a pie chart.
(a)Work out the angle for Action.(1)
(b)Work out the angle for Comedy.(1)
(c)Work out the angle for Horror.(1)
(d)Work out the angle for Romance.(1)
(e)Show that your four angles add up to 360 degrees.(2)
(Total for Question 9 is 6 marks)
10
Using your angles from Question 9 and the blank circle below, draw and label a pie chart to show the film genre data. Use a protractor to measure each angle from the 0 degree line shown, working clockwise, in the order Action, Comedy, Horror, Romance.
(Total for Question 10 is 3 marks)
11
120 vehicles passing a checkpoint were counted and classified. The pie chart shows the results, with the angle of each sector written on the chart.
(a)Work out the number of vans.(2)
(b)Work out the percentage of vehicles that were motorbikes.(2)
(Total for Question 11 is 4 marks)
12
An orchard survey recorded the type of every fruit tree planted. The pie chart shows the results, with two of the sector angles written on the chart. There were 15 apple trees.
(a)Work out the total number of trees in the orchard.(2)
(b)Work out the number of pear trees.(2)
(c)State one assumption you must make in order for your answer to part (b) to be correct.(1)
(Total for Question 12 is 5 marks)
13
A researcher has collected data on the favourite music genre of pupils across 12 different age groups. She is deciding whether to present the data as a pie chart or as a bar chart.
(a)Give one advantage of using a pie chart, rather than a bar chart, to display data for a single age group.(1)
(b)Give one disadvantage of using a pie chart, rather than a bar chart, to display data for a single age group.(1)
(c)The researcher has 12 different age groups to compare. Explain why a pie chart might not be a good choice for displaying this particular data set.(2)
(Total for Question 13 is 4 marks)
14
200 shoppers were asked how they paid for their shopping. The pie chart shows the results, with the percentage for each payment method written on each sector.
(a)Work out the angle that represents Cash on the pie chart.(2)
(b)Work out the number of shoppers who paid by contactless.(2)
(Total for Question 14 is 4 marks)
15
Two pie charts show the favourite holiday destination chosen by pupils in Year 10 (120 pupils) and Year 11 (90 pupils). Each pie chart shows the angle of the sector for Beach; the rest of each chart is grouped as Other destinations.
(a)Write down which year group's pie chart has the larger angle for Beach.(1)
(b)Work out the number of Year 10 pupils who chose Beach.(2)
(c)Work out the number of Year 11 pupils who chose Beach.(2)
(d)Even though the angle for Beach is larger on the Year 11 pie chart, use your answers to parts (b) and (c) to explain which year group actually had more pupils choose Beach.(1)
(Total for Question 15 is 6 marks)
16
Amir wants to find out how pupils in his school year travel to school. He plans to survey 60 pupils.
(a)Write a suitable survey question Amir could use to collect this data.(1)
(b)Amir collects the data and organises it into the frequency table below.
Method
Walk
Cycle
Bus
Car
Frequency
24
6
18
12
Calculate the angle needed to represent Cycle in a pie chart.(2)
(c)Amir then draws the pie chart shown above from his full results. He claims: 'More than a third of the pupils travel to school by bus.' Use the pie chart to decide whether Amir's claim is correct. You must show your working.(2)
(Total for Question 16 is 5 marks)
17
A survey of 180 people asked which type of music they liked best. The pie chart shows the results. The sector for Classical and Jazz combined has not been split further, but it is known that the number of people who chose Classical was twice the number who chose Jazz.
(a)Work out the number of people who chose Pop.(2)
(b)Work out the number of people who chose Rock.(1)
(c)Work out the total number of people who chose Classical or Jazz.(1)
(d)Given that the number of people who chose Classical was twice the number who chose Jazz, work out the number of people who chose Jazz.(2)
(Total for Question 17 is 6 marks)
18
The diagram below shows the same type of data drawn as a 3D-style pie chart, tilted at an angle.
Explain one reason why a 3D-style pie chart like this can be misleading compared to a standard 2D pie chart.
(Total for Question 18 is 2 marks)
Mark scheme · S21 Pie Charts
Question 1
(i) B1 True cao
(i) Answer: True
(ii) B1 False cao
(ii) Answer: False
Question 2
(a) B1 Football cao
(a) Answer: Football
(b) M1 12 + 8 + 5 + 5, oe (adds all four frequencies)
(b) A1 30 cao
(b) Answer: 30
Question 3
(a) B1 Mint cao
(a) Answer: Mint
(b) M1 10% of 50, oe, e.g. 0.10 x 50
(b) A1 5 cao
(b) Answer: 5
Question 4
(a) B1 Blue cao
(a) Answer: Blue
(b) B1 Red cao
(b) Answer: Red
(c) B1 1/5 oe cao
(c) Answer: 1/5
Question 5
(a) M1 4/30 seen, oe
(a) A1 2/15 cao
(a) Answer: 2/15
(b) B1 2/5 cao
(b) Answer: 2/5
Question 6
(a) M1 15/60 x 360, oe
(a) A1 90 (degrees) cao
(a) Answer: 90 degrees
(b) B1 the pie chart is a full circle (360 deg) that represents the whole sample/everyone surveyed, oe
(b) Answer: The whole circle (360 degrees) represents all 60 people surveyed, so the four sectors must share out all 360 degrees between them.
Question 7
M1 23/70 x 360, oe
A1 awrt 118 (degrees)
Answer: 118 degrees (nearest degree)
Question 8
M1 130 + 110 + 90 + 40, oe (adds the four angles)
A1 370 found and compared to 360 (angles in a pie chart must sum to 360 deg), so there is an error
Answer: 130+110+90+40 = 370, which is not 360, so the angles cannot be correct.
Question 9
(a) B1 120 (degrees) cao
(a) Answer: 120 degrees
(b) B1 80 (degrees) cao
(b) Answer: 80 degrees
(c) B1 60 (degrees) cao
(c) Answer: 60 degrees
(d) B1 100 (degrees) cao
(d) Answer: 100 degrees
(e) M1 120 + 80 + 60 + 100, oe (adds all four angles from a-d)
(e) A1 360 shown/confirmed
(e) Answer: 120+80+60+100 = 360
Question 10
B1 first sector (Action, 120 deg) drawn correctly from the 0 deg line, ± 2 deg
B1 remaining three sectors (Comedy 80 deg, Horror 60 deg, Romance 100 deg) drawn correctly clockwise with no gaps or overlaps, ± 2 deg each
B1 all four sectors clearly labelled with their genre names
Answer: Sectors of 120 deg (Action), 80 deg (Comedy), 60 deg (Horror) and 100 deg (Romance), drawn clockwise from the 0 deg line and labelled.
Question 11
(a) M1 90/360 x 120, oe
(a) A1 30 cao
(a) Answer: 30
(b) M1 18/360 x 100, oe
(b) A1 5% cao
(b) Answer: 5%
Question 12
(a) M1 15 / (60/360), oe, e.g. 360/60 (=6) then 15 x 6
(a) A1 90 cao
(a) Answer: 90
(b) M1 120/360 x 90, oe (ft their total from (a))
(b) A1 30 cao
(b) Answer: 30
(c) B1 that the pie chart has been drawn accurately/to scale, so each sector angle is exactly proportional to its frequency, oe
(c) Answer: The pie chart has been drawn accurately, so the sector angles are exactly proportional to the number of trees.
Question 13
(a) B1 a pie chart shows each category as a clear proportion/fraction/percentage of the whole set, which is easy to compare visually, oe
(a) Answer: A pie chart shows immediately how each genre's popularity compares as a share of the whole group, without needing a frequency scale.
(b) B1 it is harder to read off exact frequencies from a pie chart than from a bar chart with a labelled frequency axis, oe
(b) Answer: It is harder to read exact numbers of pupils straight from a pie chart, since there is no frequency scale like a bar chart's axis.
(c) B1 with 12 categories, many sectors would be small and/or similar in size to each other
(c) B1 so it becomes hard to distinguish/compare/label the sectors clearly, oe (dependent on identifying many small sectors)
(c) Answer: With 12 age groups, many sectors would be small and close in size, making them difficult to tell apart, label clearly or compare accurately.
Question 14
(a) M1 25/100 x 360, oe
(a) A1 90 (degrees) cao
(a) Answer: 90 degrees
(b) M1 20/100 x 200, oe
(b) A1 40 cao
(b) Answer: 40
Question 15
(a) B1 Year 11 cao
(a) Answer: Year 11
(b) M1 120/360 x 120, oe
(b) A1 40 cao
(b) Answer: 40
(c) M1 144/360 x 90, oe
(c) A1 36 cao
(c) Answer: 36
(d) B1 Year 10, since 40 > 36, oe; because the two pie charts represent different total numbers of pupils, so a bigger angle does not always mean a bigger frequency
(d) Answer: Year 10, because 40 pupils chose Beach compared with only 36 in Year 11, even though Year 11's sector has the bigger angle, since the two pie charts do not represent the same total number of pupils.
Question 16
(a) B1 a closed question with clear, non-overlapping response options covering all methods, e.g. 'How do you usually travel to school? Walk / Cycle / Bus / Car (tick one box)'
(a) Answer: How do you usually travel to school? Walk / Cycle / Bus / Car (tick one box)
(b) M1 6/60 x 360, oe
(b) A1 36 (degrees) cao
(b) Answer: 36 degrees
(c) B1 a third of 360 deg is 120 deg (or 18/60 = 30% found), compared correctly with the Bus angle of 108 deg
(c) B1 correct conclusion: Amir's claim is incorrect, since 108 deg < 120 deg (30% < 33.3%)
(c) Answer: Amir's claim is incorrect: the Bus sector is 108 degrees, which is less than a third of 360 degrees (120 degrees).
Question 17
(a) M1 150/360 x 180, oe
(a) A1 75 cao
(a) Answer: 75
(b) B1 45 cao
(b) Answer: 45
(c) B1 60 cao, ft 180 - their (a) - their (b)
(c) Answer: 60
(d) M1 60 shared in the ratio 2:1 (3 parts), oe, e.g. 60/3
(d) A1 20 cao
(d) Answer: 20
Question 18
B1 identifies that tilting the chart distorts the apparent area of sectors (sectors are stretched/squashed by the perspective)
B1 develops this to explain the consequence, e.g. sectors nearer the front/bottom of the tilt look bigger than their true angle/proportion suggests, making it harder to compare categories fairly
Answer: Tilting the pie chart in 3D distorts the sectors so that some (e.g. those at the front) appear larger than their true proportion, while others appear smaller, making accurate comparisons between categories difficult.