Data Interpretation: Pie Charts
CSAT · Data Interpretation
Introduction
Data interpretation (pie charts) questions give you data and ask for quick, accurate calculations. They need no outside knowledge, so they are reliable marks once the reading and arithmetic are disciplined.
Key concepts
How a pie chart works
A pie chart shows how a total is divided. Shares are given as percentages (adding to 100) or as angles (adding to 360°).
Conversions
- Angle = percentage × 3.6 (because 360/100 = 3.6).
- Percentage = angle ÷ 3.6.
- Amount = percentage × total ÷ 100.
Typical questions
| Question | Approach |
|---|---|
| Amount spent on an item | share% × total |
| Central angle of a sector | share% × 3.6 |
| Difference between two items | difference in % × total |
| Ratio of two items | ratio of their percentages |
| Effect of a change in the total | new total × same % |
Two pie charts
When two pies have different totals, compare amounts, not percentages – 20% of ₹1 lakh is more than 25% of ₹60,000.
Converting between degrees and percentages
A full circle is 360° = 100%, so 1% = 3.6° and 1° = 0.2778%. A sector of 72° is 72 ÷ 3.6 = 20% of the total. If the total budget is known, a sector's value is (percentage ÷ 100) × total.
Comparing two pie charts
Two pie charts with different totals cannot be compared by percentages alone. A sector that is 20% of ₹500 crore (₹100 crore) is larger than one that is 25% of ₹300 crore (₹75 crore). Always convert to absolute values first.
Quick checks
The percentages must add up to 100; the degrees to 360. Use this to find a missing sector before answering. Sector ratios equal percentage ratios, so a 30% sector is 1.5 times a 20% sector regardless of the total.
- % change = (new − old)/old × 100
- Share = part/total × 100
- Average = sum/count
- Pie angle = % × 3.6
Solved examples
Data set: Family budget
| Head | Share % |
|---|---|
| Food | 20 |
| Rent | 20 |
| Education | 5 |
| Transport | 25 |
| Savings | 12 |
| Others | 18 |
Example 1
How much does the family spend on Rent each month?
(a) ₹10000 (b) ₹2500 (c) ₹10500 (d) ₹5000
- 20% of ₹50,000 = ₹10000.
Answer: (a) ₹10000
Example 2
What is the central angle of the Others sector in the pie chart?
(a) 18° (b) 82 4/5° (c) 129 3/5° (d) 64 4/5°
- Central angle = share% × 360/100 = share% × 3.6.
- 18 × 3.6 = 64 4/5°.
Answer: (d) 64 4/5°
Example 3
How much more is spent on Others than on Savings each month?
(a) ₹15000 (b) ₹4000 (c) ₹3000 (d) ₹6000
- Difference in share = 6%.
- 6% of ₹50,000 = ₹3000.
Answer: (c) ₹3000
Example 4
If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹11000 (b) ₹6600 (c) ₹6000 (d) ₹7100
- New income = ₹55000.
- Savings = 12% × 55000 = ₹6600.
Answer: (b) ₹6600
Data set: Family budget
| Head | Share % |
|---|---|
| Food | 8 |
| Rent | 12 |
| Education | 8 |
| Transport | 30 |
| Savings | 12 |
| Others | 30 |
Example 5
How much does the family spend on Education each month?
(a) ₹6400 (b) ₹24000 (c) ₹7200 (d) ₹3200
- 8% of ₹80,000 = ₹6400.
Answer: (a) ₹6400
Example 6
What is the central angle of the Education sector in the pie chart?
(a) 46 4/5° (b) 57 3/5° (c) 28 4/5° (d) 8°
- Central angle = share% × 360/100 = share% × 3.6.
- 8 × 3.6 = 28 4/5°.
Answer: (c) 28 4/5°
Example 7
How much more is spent on Transport than on Savings each month?
(a) ₹28800 (b) ₹14400 (c) ₹33600 (d) ₹15400
- Difference in share = 18%.
- 18% of ₹80,000 = ₹14400.
Answer: (b) ₹14400
Example 8
If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹11060 (b) ₹17600 (c) ₹9600 (d) ₹10560
- New income = ₹88000.
- Savings = 12% × 88000 = ₹10560.
Answer: (d) ₹10560
Data set: Family budget
| Head | Share % |
|---|---|
| Food | 8 |
| Rent | 30 |
| Education | 20 |
| Transport | 5 |
| Savings | 15 |
| Others | 22 |
Example 9
How much does the family spend on Food each month?
(a) ₹18000 (b) ₹2400 (c) ₹4800 (d) ₹5400
- 8% of ₹60,000 = ₹4800.
Answer: (c) ₹4800
Example 10
What is the central angle of the Rent sector in the pie chart?
(a) 30° (b) 108° (c) 126° (d) 216°
- Central angle = share% × 360/100 = share% × 3.6.
- 30 × 3.6 = 108°.
Answer: (b) 108°
Example 11
How much more is spent on Rent than on Savings each month?
(a) ₹27000 (b) ₹18000 (c) ₹10000 (d) ₹9000
- Difference in share = 15%.
- 15% of ₹60,000 = ₹9000.
Answer: (d) ₹9000
Example 12
If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹9900 (b) ₹9000 (c) ₹10400 (d) ₹15000
- New income = ₹66000.
- Savings = 15% × 66000 = ₹9900.
Answer: (a) ₹9900
Data set: Family budget
| Head | Share % |
|---|---|
| Food | 15 |
| Rent | 30 |
| Education | 15 |
| Transport | 12 |
| Savings | 10 |
| Others | 18 |
Example 13
How much does the family spend on Savings each month?
(a) ₹12960 (b) ₹3600 (c) ₹7200 (d) ₹7920
- 10% of ₹72,000 = ₹7200.
Answer: (c) ₹7200
Example 14
What is the central angle of the Food sector in the pie chart?
(a) 54° (b) 108° (c) 72° (d) 15°
- Central angle = share% × 360/100 = share% × 3.6.
- 15 × 3.6 = 54°.
Answer: (a) 54°
Example 15
How much more is spent on Education than on Transport each month?
(a) ₹19440 (b) ₹2160 (c) ₹4320 (d) ₹3160
- Difference in share = 3%.
- 3% of ₹72,000 = ₹2160.
Answer: (b) ₹2160
Example 16
If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹8420 (b) ₹7200 (c) ₹14400 (d) ₹7920
- New income = ₹79200.
- Savings = 10% × 79200 = ₹7920.
Answer: (d) ₹7920
- Read all questions on a set before calculating – reuse totals.
- Approximate when options are far apart; compute exactly when they are close.
- Write intermediate numbers in a mini-table.
- Using the wrong base for percentage change.
- Ignoring units (thousands, crore, %).
- Confusing absolute and percentage changes.
Practice set
Use the chart or table for each set; about 90 seconds per question.
Practice data: Family budget
| Head | Share % |
|---|---|
| Food | 12 |
| Rent | 20 |
| Education | 15 |
| Transport | 25 |
| Savings | 20 |
| Others | 8 |
Q1. How much does the family spend on Education each month?
(a) ₹20000 (b) ₹12800 (c) ₹6000 (d) ₹12000
Q2. What is the central angle of the Rent sector in the pie chart?
(a) 144° (b) 90° (c) 72° (d) 20°
Q3. How much more is spent on Transport than on Education each month?
(a) ₹8000 (b) ₹9000 (c) ₹16000 (d) ₹32000
Q4. If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹18100 (b) ₹17600 (c) ₹16000 (d) ₹24000
Practice data: Family budget
| Head | Share % |
|---|---|
| Food | 15 |
| Rent | 5 |
| Education | 10 |
| Transport | 15 |
| Savings | 8 |
| Others | 47 |
Q5. How much does the family spend on Education each month?
(a) ₹4400 (b) ₹6000 (c) ₹2000 (d) ₹4000
Q6. What is the central angle of the Transport sector in the pie chart?
(a) 54° (b) 72° (c) 108° (d) 15°
Q7. How much more is spent on Others than on Education each month?
(a) ₹15800 (b) ₹29600 (c) ₹14800 (d) ₹22800
Q8. If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹4020 (b) ₹3520 (c) ₹7200 (d) ₹3200
Practice data: Family budget
| Head | Share % |
|---|---|
| Food | 5 |
| Rent | 10 |
| Education | 8 |
| Transport | 25 |
| Savings | 8 |
| Others | 44 |
Q9. How much does the family spend on Transport each month?
(a) ₹10000 (b) ₹3200 (c) ₹10400 (d) ₹5000
Q10. What is the central angle of the Education sector in the pie chart?
(a) 57 3/5° (b) 28 4/5° (c) 46 4/5° (d) 8°
Q11. How much more is spent on Rent than on Savings each month?
(a) ₹7200 (b) ₹1600 (c) ₹800 (d) ₹1800
Q12. If income rises by 10% and the percentage shares stay the same, what are the new monthly savings?
(a) ₹4020 (b) ₹3200 (c) ₹7200 (d) ₹3520
Q1 – (d) ₹12000. 15% of ₹80,000 = ₹12000.
Q2 – (c) 72°. Central angle = share% × 360/100 = share% × 3.6. 20 × 3.6 = 72°.
Q3 – (a) ₹8000. Difference in share = 10%. 10% of ₹80,000 = ₹8000.
Q4 – (b) ₹17600. New income = ₹88000. Savings = 20% × 88000 = ₹17600.
Q5 – (d) ₹4000. 10% of ₹40,000 = ₹4000.
Q6 – (a) 54°. Central angle = share% × 360/100 = share% × 3.6. 15 × 3.6 = 54°.
Q7 – (c) ₹14800. Difference in share = 37%. 37% of ₹40,000 = ₹14800.
Q8 – (b) ₹3520. New income = ₹44000. Savings = 8% × 44000 = ₹3520.
Q9 – (a) ₹10000. 25% of ₹40,000 = ₹10000.
Q10 – (b) 28 4/5°. Central angle = share% × 360/100 = share% × 3.6. 8 × 3.6 = 28 4/5°.
Q11 – (c) ₹800. Difference in share = 2%. 2% of ₹40,000 = ₹800.
Q12 – (d) ₹3520. New income = ₹44000. Savings = 8% × 44000 = ₹3520.
- Units and base first
- % change on the old value
- Reuse totals
- Approximate wisely
