Data Interpretation: Charts, Tables, and Solved PSC Problems
Complete guide to data interpretation for Kerala PSC — reading bar charts, pie charts, line graphs, and tables with 10 solved problems in exam pattern.
Complete guide to data interpretation for Kerala PSC — reading bar charts, pie charts, line graphs, and tables with 10 solved problems in exam pattern.
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Data Interpretation (DI) questions appear in every PSC Graduate Level exam — typically 3-5 questions based on a single chart or table. This note covers chart types, reading strategies, and 10 solved problems.
Types of Data Representation
| Type | Best For | Key Reading Skill |
|---|---|---|
| Bar Chart | Comparing quantities across categories | Read height/length against Y-axis |
| Pie Chart | Showing parts of a whole (%) | Calculate degree/percentage of each sector |
| Line Graph | Showing trends over time | Identify increase/decrease/constant periods |
| Table | Exact values across multiple parameters | Cross-reference rows and columns |
| Stacked Bar | Comparing composition of categories | Read segment heights within bars |
Essential Formulas
| Formula | Expression |
|---|---|
| Percentage | (Part / Whole) x 100 |
| Percentage change | ((New - Old) / Old) x 100 |
| Average (Mean) | Sum of all values / Number of values |
| Ratio | A : B (simplify by dividing both by HCF) |
| Degree in pie chart | (Value / Total) x 360 |
| Value from pie degree | (Degree / 360) x Total |
Pie Chart Rules
- Full circle = 360 degrees = 100%
- 1% = 3.6 degrees
- To find value: (Sector degree / 360) x Total value
- To find degree: (Value / Total) x 360
Solved Problem Set
Problem 1: Bar Chart — Production of a Factory
A factory’s production (in thousand units) over 5 years:
| Year | Production (thousand units) |
|---|---|
| 2019 | 45 |
| 2020 | 30 |
| 2021 | 50 |
| 2022 | 55 |
| 2023 | 60 |
Q1: What is the percentage increase in production from 2020 to 2021?
Solution: Increase = 50 - 30 = 20 thousand Percentage = (20/30) x 100 = 66.67%
Q2: What is the average production over 5 years?
Solution: Total = 45 + 30 + 50 + 55 + 60 = 240 Average = 240/5 = 48 thousand units
Problem 2: Pie Chart — Monthly Expenditure
A family’s monthly expenditure of Rs. 36,000:
| Category | Degree |
|---|---|
| Food | 120 |
| Rent | 90 |
| Education | 60 |
| Transport | 40 |
| Savings | 30 |
| Others | 20 |
| Total | 360 |
Q3: How much is spent on Food?
Solution: (120/360) x 36,000 = Rs. 12,000
Q4: What percentage of income is saved?
Solution: (30/360) x 100 = 8.33%
Q5: Ratio of expenditure on Education to Rent?
Solution: Education : Rent = 60 : 90 = 2 : 3
Problem 3: Table — Marks of Students
| Student | Maths | Science | English | Total |
|---|---|---|---|---|
| Arun | 85 | 78 | 72 | 235 |
| Binu | 70 | 82 | 88 | 240 |
| Chinnu | 92 | 65 | 80 | 237 |
| Deepa | 78 | 90 | 75 | 243 |
| Elsa | 65 | 75 | 95 | 235 |
Q6: Who scored the highest in total?
Solution: Deepa (243)
Q7: What is the average marks in Science for all students?
Solution: (78 + 82 + 65 + 90 + 75) / 5 = 390/5 = 78
Q8: Difference between highest and lowest total marks?
Solution: 243 - 235 = 8
Problem 4: Line Graph — Temperature Over a Week
| Day | Temperature (C) |
|---|---|
| Mon | 28 |
| Tue | 30 |
| Wed | 32 |
| Thu | 35 |
| Fri | 33 |
| Sat | 29 |
| Sun | 27 |
Q9: On which day was the maximum rise in temperature compared to previous day?
Solution: Compare daily changes:
- Mon to Tue: +2
- Tue to Wed: +2
- Wed to Thu: +3 (maximum rise)
- Thu to Fri: -2
- Fri to Sat: -4
- Sat to Sun: -2
Answer: Thursday (rise of 3 degrees)
Q10: What is the average temperature for the week?
Solution: Total = 28 + 30 + 32 + 35 + 33 + 29 + 27 = 214 Average = 214/7 = 30.57 C (approximately 30.6 C)
Practice Strategies for PSC DI Questions
Step-by-Step Approach
| Step | Action |
|---|---|
| 1 | Read the title and understand what the data represents |
| 2 | Note units (thousands, lakhs, crores, %) |
| 3 | Read the question carefully — what is asked? |
| 4 | Identify relevant data points from chart/table |
| 5 | Apply appropriate formula |
| 6 | Check if answer matches one of the options |
Common Traps in PSC DI Questions
| Trap | How to Avoid |
|---|---|
| Units confusion | Always check — “in thousands” means multiply answer by 1000 |
| Percentage OF vs percentage INCREASE | ”What % is A of B” differs from ”% increase from B to A” |
| Wrong base for % change | Always divide by OLD value for % change |
| Reading wrong bar/segment | Double-check category labels and legend |
| Approximate vs exact | PSC usually gives exact-match options; calculate precisely |
Quick Calculation Tips
| Technique | Application |
|---|---|
| 1/2 = 50% | Quick conversion |
| 1/3 = 33.33% | Memorise common fractions |
| 1/4 = 25% | - |
| 1/5 = 20% | - |
| 1/6 = 16.67% | - |
| 1/8 = 12.5% | - |
| Multiplying by 5 | Multiply by 10, divide by 2 |
| Finding 15% | Find 10% + half of 10% |
| Finding 12.5% | Divide by 8 |
Additional Practice Problem Types
Type 1: Growth Rate Questions
“If production in 2022 was 500 units and grew by 20% in 2023, what was 2023 production?”
Solution: 500 + (20% of 500) = 500 + 100 = 600 units
Type 2: Ratio from Pie Chart
“If A:B:C in a pie chart are 90:120:150 degrees, express as simplest ratio.”
Solution: 90:120:150 = 3:4:5
Type 3: Missing Value
“Average of 5 numbers is 42. Four numbers are 38, 44, 40, 46. Find the fifth.”
Solution: Total = 42 x 5 = 210. Fifth = 210 - (38+44+40+46) = 210 - 168 = 42
PSC Question Patterns
| Pattern | What They Test |
|---|---|
| ”What is the ratio of X to Y?” | Reading values and simplifying |
| ”Percentage increase/decrease from year A to B” | Formula application |
| ”Average of given values” | Sum and divide |
| ”Which year shows maximum growth?” | Compare consecutive differences |
| ”What fraction/part of total is X?” | Part-to-whole calculation |
| ”If total is N, find value of sector” | Pie chart degree to value conversion |
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