Pie Chart
Comprehensive notes, formulas, and practice questions for Pie Chart.
Pie Chart
Pie Chart
What you'll learn
- How pie charts show part-to-whole relationships using central angles and sector areas.
- To convert between degrees, percentages, and absolute values given the total.
- To compare sectors and solve "how much more" questions on budget and expenditure pies.
- To combine pie charts with tables when totals differ between groups.
Key concepts
Level 1 — Foundations
Verbal: A full circle = 360° = 100% of the whole. Each slice (sector) represents a category's share.
Conversion formulas:
| Given | Find | Formula |
|---|---|---|
| Percent p | Central angle | (p/100) × 360° |
| Angle θ | Percent | (θ/360) × 100 |
| Percent p, total T | Value | (p/100) × T |
| Value v, total T | Percent | (v/T) × 100 |
Reading tips: Larger slice → larger share. Labels may show % directly or only category name — use protractor only if exam allows; usually angles are nice numbers (90°, 120°).
Multi-pie problems: Two pies with different totals — do not compare slice angles across pies for absolute amounts; compare percentages then multiply by respective totals.
Level 2 — Exam depth
Semi-pie / doughnut: Same math; missing slice may mean "other" or omitted category — read caption.
Exploded slice: Emphasis only; angle unchanged unless stated otherwise.
Reverse engineering total: If Food = ₹450 and angle = 90°, total = 450 × (360/90) = ₹1800.
Average sector: Mean of percents only equals meaningful "average category" if categories are equally weighted — usually not the same as average of values.
Combined with bar graph: Pie for composition, bar for trend over time — common two-chart DI sets in exams.
Worked example
Find expenditure from angle and total budget
Monthly budget = ₹36,000. Rent sector = 120°.
Step 1 — Rent percent = 120/360 × 100 = 33⅓%.
Step 2 — Rent amount = (1/3) × 36,000 = **₹12,000**.
Step 3 — Check: remaining 240° = ₹24,000 ✓
Compare two categories from degrees
Transport = 72°, Education = 54° on same pie.
Difference in share = (72−54)/360 × 100 = 5%.
If total income ₹50,000, Transport exceeds Education by 5% of 50,000 = **₹2,500**.
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Using 180° as 100% | Confused with semicircle | Full pie = 360° = 100% |
| Comparing slice sizes across two pies with different totals | Angles equal ⇒ values equal | Convert % then multiply by each total |
| Rounding angles too early | Lost precision | Keep fractions until final step |
| Forgetting 'Other' slice | Percent sum < 100% | Add all sectors; find missing share |
Quick check
- A sector is 90° — what percent and what fraction of the whole?
- Total 800 students; Sports 25% — how many students?
- Rent 110°, Food 130° — can remaining sectors include a 150° slice? Why?
- Stretch: Pie shows 2023 only; bar shows 2020–2023 trend — list two questions you can/cannot answer.
Revision tip: Revisit adjacent topics in Data Interpretation before mixed practice on Pie Chart.
Open the Practice tab for graded questions on Pie Chart.
Exam strategy
Memorise the angle–percent table: 30°=8⅓%, 45°=12.5%, 60°=16⅔%, 90°=25%, 120°=33⅓%, 180°=50%. On compound questions, convert all sectors to amounts using the stated total before comparing across categories. If only two sector angles are given and the rest is "Other", subtract from 360° first. Check that sector percentages sum to 100% within rounding tolerance.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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