Angles and areas: pie charts and bubbles
A pie splits one whole into shares, so its angles follow the percentages. A bubble's area, not its radius, should match its value.
A pie chart divides one total into shares. W6 p. 4: Physics 100 and Computing 400 students, total 500. Shares are 100/500=20% and 400/500=80%; slice angles are 0.20×360°=72° and 0.80×360°=288°. Slices share one radius, so angle and area both represent the share. A pie is appropriate only when the parts form a meaningful whole that adds to 100% and there are few slices. To compare categories with each other, or across several groups, bars on a common axis are usually easier to read than similar angles.
A bubble should encode its value by area. W6 p. 5: Computing 400 is four times Physics 100, so the area ratio must be 4. Because A=πr², the radius ratio is √4=2: example radii 10 and 20. In general, radius ∝ √value.
Common error: scaling the radius by the value. A radius four times as large creates an area 4²=16 times as large, so a 4× difference is drawn as 16×. When software asks for a marker "size", check whether it means area or radius (matplotlib's s in scatter is an area in points²).
Source: W6 PDF pp. 1-37. Most numbers in the lecture are illustrative or constructed for teaching; pp. 26-27 reuse the Week 5 synthetic registration counts. The Week 6 lab manual (L6) practises Week 5 EDA reasoning and is worked through section by section in Lab work.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
Physics has 100 students out of 500. What is its pie-slice angle?
A bubble represents four times another bubble's value. By what factor should its radius grow?
2. Application
Apply the concept to a case or calculation.
Computing has 400 of 500 students. What is its slice angle?
When is a pie chart appropriate?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
A designer makes one bubble's radius 4 times another's for a 4× value. How much larger is its area?
Physics 100 is drawn with radius 10. What radius should Computing 400 have?
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Its area should be 4 times as large. Since area=πr², its radius should be √4=2 times as large.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
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When readers must compare categories with each other or across groups, when there are many categories, or when the values do not form one whole. Lengths on a common axis are easier to compare than similar angles.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?