Comparative and Proportional Pie Charts
Comparative, or proportional, pie charts are pairs or sets of pie charts used to compare data sets of different total sizes, where the radius of each chart is scaled so its area reflects the size of the total frequency it represents. This means a data set with a much larger total is drawn as a visibly bigger pie chart, in addition to each chart's own sector angles showing its own internal proportions.
Before you start
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Method
- Find the total frequency represented by each pie chart, for example the total number of people surveyed in each group.
- To compare the data sets fairly, the area of each pie chart should be proportional to its total frequency, so the ratio of the radii equals the square root of the ratio of the frequencies: r2/r1 = sqrt(total2/total1).
- Choose a radius for one pie chart, then use this ratio to calculate the radius for the other pie chart or charts.
- Within each pie chart, calculate each sector's angle in the usual way: angle = (category frequency / that chart's own total frequency) x 360 degrees.
- Draw or interpret each pie chart with sector angles found as normal, letting the differing radii show the difference in total sample size at a glance.
- When comparing proportions between two charts, compare the sector angles or percentages, not the areas of the sectors, since equal angles in charts of different radii still represent equal proportions of their own totals.
Worked example
A survey of 50 people in Town A and 200 people in Town B asked about preferred mode of transport. A comparative pie chart is to be drawn, with the pie chart for Town A having radius 3 cm. Calculate the radius of the pie chart for Town B.
- Ratio of totals = 200/50 = 4.
- Ratio of radii = sqrt(4) = 2.
- Radius for Town B = 3 x 2 = 6 cm.
- Final answer: 6 cm.
Practice questions
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Q1Two pie charts represent totals of 40 and 160. If the smaller chart has radius 2 cm, find the radius of the larger chart.Show answer
Answer: 4 cm (ratio 160/40=4, sqrt(4)=2, so 2 x 2)
Q2Two pie charts represent totals of 25 and 100. The smaller has radius 3 cm. Find the radius of the larger.Show answer
Answer: 6 cm (ratio 100/25=4, sqrt(4)=2, so 3 x 2)
Q3A comparative pie chart pair has radii 4 cm and 8 cm. Find the ratio of the totals they represent.Show answer
Answer: 1 : 4 ((8/4)^2 = 4)
Q4In a pie chart for Class A (30 pupils), 12 pupils chose football. Find the sector angle for football.Show answer
Answer: 144 degrees ((12/30) x 360)
Q5In a comparative pie chart, Class A (30 pupils) has a football sector of 144 degrees and Class B (60 pupils) has a football sector of 90 degrees. Which class has the greater proportion of pupils choosing football?Show answer
Answer: Class A (144/360 = 40 percent, compared with 90/360 = 25 percent for Class B)
Q6Two comparative pie charts have totals of 18 and 72. If the pie chart for the total of 18 has radius 2.5 cm, find the radius of the other pie chart.Show answer
Answer: 5 cm (ratio 72/18=4, sqrt(4)=2, so 2.5 x 2)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A survey of 60 customers at Shop A and 240 customers at Shop B recorded their favourite drink. Comparative pie charts are to be drawn, with the pie chart for Shop A given a radius of 4 cm. Calculate the radius that should be used for Shop B's pie chart.
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Two comparative pie charts represent surveys of 45 students in School X and 180 students in School Y. In School X's pie chart, the sector for 'walk to school' has an angle of 80 degrees. (a) Find the ratio of the radii of the two pie charts, giving School X's pie chart a radius of 1 unit. (b) Given that 36 students in School Y walk to school, calculate the sector angle for 'walk to school' in School Y's pie chart, and state whether a greater proportion of students walk to school in School X or School Y.
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Explain why, when comparing two data sets of very different sizes using pie charts, it is more appropriate to draw comparative pie charts of different radii rather than two pie charts of the same radius.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the comparative and proportional pie charts worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 14 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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