Data Interpretation: Pie Charts, Caselets and Mixed Sets
Data Interpretation: Pie Charts, Caselets and Mixed Sets
A pie chart splits a whole into sectors, given either as percentages or as central angles out of 360°. A caselet gives the same kind of data as a paragraph that you must turn into a table. Mixed sets combine two displays, typically a pie chart for the totals and a table for the split within each part.
1. Conversion Box
Central angle = (percentage/100) × 360° = percentage × 3.6
Percentage = (central angle/360°) × 100
Value of a sector = (its percentage/100) × total = (its angle/360°) × total
Two sectors compared: value ratio = percentage ratio = angle ratio (the total cancels)
| Percentage | 5% | 10% | 12.5% | 20% | 25% | 30% | 50% |
|---|---|---|---|---|---|---|---|
| Central angle | 18° | 36° | 45° | 72° | 90° | 108° | 180° |
Caselet with two overlapping groups: only A = A − both; either = A + B − both; neither = total − either
✗ A 63° sector is 63% of the total | ✓ 63/360 × 100 = 17.5%
✗ In a caselet, students liking cricket or football = 35 + 28 | ✓ Subtract those counted twice: 35 + 28 − 10 = 53
हिंदी नोट: वृत्त आलेख में केंद्रीय कोण = प्रतिशत × 3.6 और प्रतिशत = कोण ÷ 3.6। दो भागों की तुलना के लिए कुल मान की ज़रूरत नहीं, कोणों या प्रतिशत का अनुपात ही काफ़ी है।
Exam Pointer: Verified NTPC pattern: converting a pie-chart central angle into a percentage of the total (June 2022 CBT-2). Sector values, caselets and mixed sets had no verified NTPC shift in our check and are tagged syllabus-based.
2. Data Sets
Pie chart: cost of publishing a book (percentage of total cost).
| Item | Paper | Printing | Binding | Royalty | Transport | Advertisement |
|---|---|---|---|---|---|---|
| Share | 25% | 20% | 15% | 15% | 10% | 15% |
Mixed set: a school of 1,200 students. Pie chart of students by class, with a table of the boys : girls ratio in each class.
| Class | VI | VII | VIII | IX | X |
|---|---|---|---|---|---|
| Share of students | 15% | 20% | 25% | 22% | 18% |
| Boys : Girls | 1 : 1 | 3 : 5 | 7 : 8 | 5 : 6 | 1 : 2 |
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Central angle and percentage
[PYQ: NTPC CBT-2 15-Jun-2022 Shift-3]
EXAM LEVEL
Q. A sector of a pie chart has a central angle of 72°. What percentage of the total does it show?
72/360 × 100 = 20%.
Answer: 20%
EXAMATLAS LEVEL
Q. A family's monthly expenses of ₹48,000 are shown in a pie chart. Food takes 30% and Rent has a central angle of 90°. Find the central angle for Food and how much more is spent on Food than on Rent.
Food angle = 30 × 3.6 = 108°. Food = 30% of 48,000 = ₹14,400. Rent = 90/360 = 25% = ₹12,000. Difference = ₹2,400.
Answer: 108°; ₹2,400
Pattern 2: Value of a sector from another sector or the total
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. From the publishing pie chart, if the royalty paid is ₹30,000, what is the cost of paper?
Paper : Royalty = 25 : 15, so paper = 30,000 × 25/15 = ₹50,000.
Answer: ₹50,000
EXAMATLAS LEVEL
Q. From the publishing pie chart, the total cost of producing 5,000 copies is ₹4,00,000 and the publisher wants a 25% profit on cost. Find the selling price per copy and the central angle for Printing and Binding together.
Total selling price = 1.25 × 4,00,000 = ₹5,00,000, so ₹100 per copy. Printing and Binding = 35%, an angle of 35 × 3.6 = 126°.
Answer: ₹100; 126°
Pattern 3: Caselets (data given as a paragraph)
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In a class of 60 students, 35 like cricket, 28 like football and 10 like both. How many like neither?
Either = 35 + 28 − 10 = 53, so neither = 60 − 53 = 7.
Answer: 7
EXAMATLAS LEVEL
Q. In a survey of 500 people, 60% read newspaper A, 50% read newspaper B and 20% read both. How many read exactly one paper, and how many read neither? If 40% of those reading only A are women, how many such women are there?
A = 300, B = 250, both = 100. Only A = 200 and only B = 150, so exactly one = 350. Either = 450, so neither = 50. Women reading only A = 40% of 200 = 80.
Answer: 350; 50; 80
Pattern 4: Mixed sets: pie chart plus table
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. From the school data, how many girls are in class VIII?
Class VIII = 25% of 1,200 = 300 students, split 7 : 8, so girls = 300 × 8/15 = 160.
Answer: 160
EXAMATLAS LEVEL
Q. From the school data, find the total number of girls in the school and the percentage of girls, and the class with the most boys.
Students: VI 180, VII 240, VIII 300, IX 264, X 216. Girls: 90, 150, 160, 144, 144, a total of 688, which is 688/1,200 ≈ 57.33%. Boys: 90, 90, 140, 120, 72, so class VIII has the most boys.
Answer: 688 girls (about 57.33%); class VIII
60-Second Revision
- Angle = % × 3.6; % = angle ÷ 3.6.
- Compare sectors by their percentages or angles directly.
- Caselets: build the table or a two-set count first; either = A + B − both.
- Mixed sets: share × total gives each part, then split by the ratio.
Next Step: Data Interpretation done. Solve one DI set a day in the ExamAtlas RRB NTPC 2026 mock tests; write the graph values in a small table first and each question takes under a minute.