31 Data Interpretation
Data interpretation (DI) is the extraction of meaning from tables, charts, and graphs through reading, calculation, and reasoning. NTA Paper-I always presents at least one DI set — typically a table or chart followed by 4–5 questions.
31.1 Working Approach to a DI Set
- Read the title and source — what does the data represent?
- Identify the units and scale — rupees in lakhs? Tonnes? Percentages?
- Note the rows and columns (or axes) — what does each represent?
- Read the questions before doing detailed calculations — focus the second pass.
- Solve simple lookups first — they are usually verifiable in seconds.
- Estimate before precise calculation — eliminates wrong options quickly.
31.2 Working Calculations
| Calculation | Formula |
|---|---|
| Percentage | (Value / Total) × 100 |
| Percentage change | ((New − Old) / Old) × 100 |
| Ratio | A : B = A / B |
| Average / Mean | Sum / Count |
| Weighted average | Σ (weight × value) / Σ weights |
| Growth rate (year on year) | ((Year2 − Year1) / Year1) × 100 |
| CAGR (compound annual growth rate) | (End/Start)^(1/n) − 1, where n = years |
| Median | Middle value when sorted |
| Pie slice value | (Angle / 360) × Total |
| Pie chart percentage | (Angle / 360) × 100 |
31.3 Reading Tables — Worked Example
Sales of a company (₹ in crores):
| Year | Product A | Product B | Product C | Total |
|---|---|---|---|---|
| 2020 | 50 | 80 | 70 | 200 |
| 2021 | 60 | 90 | 80 | 230 |
| 2022 | 75 | 95 | 80 | 250 |
| 2023 | 90 | 100 | 90 | 280 |
| 2024 | 110 | 110 | 100 | 320 |
Q. What is the percentage growth of Product A from 2020 to 2024?
Growth % = ((110 − 50) / 50) × 100 = (60/50) × 100 = 120 %.
Q. In which year did Product A contribute the highest percentage to total sales?
- 2020: 50/200 = 25 %
- 2021: 60/230 ≈ 26 %
- 2022: 75/250 = 30 %
- 2023: 90/280 ≈ 32 %
- 2024: 110/320 ≈ 34.4 %
Highest: 2024.
Q. What is the average sales of Product B over the five years?
Average = (80 + 90 + 95 + 100 + 110) / 5 = 475 / 5 = ₹95 crores.
31.4 Reading Bar Charts
- Read the y-axis carefully — note the units and scale.
- Compare bar heights, not their visual presence.
- Look for the largest, smallest, equal, and trend.
- For grouped bars: each group represents a category; bars within = sub-categories.
31.5 Reading Pie Charts
A college’s student composition by stream is shown in a pie chart with these angles: Arts 144°, Science 108°, Commerce 72°, Engineering 36°. Total students = 600.
Q. How many students are in Science?
Science share = 108/360 = 30 %. Number = 30 % of 600 = 180 students.
Q. Ratio of Arts to Engineering students?
Arts: 144°; Engineering: 36°. Ratio = 144 : 36 = 4 : 1.
31.6 Reading Line Charts
- Trace each line carefully — x-axis is usually time.
- Identify the highest and lowest points.
- Compute slope or rate of change between two points.
- Compare two lines for crossover and gap.
31.7 Common DI Question Patterns
| Pattern | What it asks | Approach |
|---|---|---|
| Direct lookup | “What was X in year Y?” | Read off the table/chart |
| Percentage / share | “What percent did X contribute?” | (X / Total) × 100 |
| Percentage change | “By how much did X grow / decline?” | ((New − Old)/Old) × 100 |
| Ratio / Comparison | “Ratio of A to B” or “A is how many times B?” | A/B |
| Average / Mean | “Average over years” | Sum / Count |
| Trend identification | “In which year was the maximum / minimum?” | Scan the data |
31.8 Estimation Techniques to Save Time
- Round generously — 2 845 ≈ 2 800; 19 % ≈ 20 %. Adjust the final answer if precision is needed.
- Compare orders of magnitude — if options differ by 10×, exact calculation is unnecessary.
- Eliminate impossible options first — DI MCQs usually have at least one obviously wrong option.
31.9 Common Pitfalls
| Pitfall | What it means |
|---|---|
| Misreading the unit | Dollars vs rupees, lakhs vs crores, tonnes vs kilograms |
| Confusing absolute and percentage | “Increase of 20” vs “Increase by 20 %” |
| Reading the wrong row/column | Especially in dense tables |
| Using the wrong base | “% increase” uses the old value as base, not the new one |
| Mixing categories | Aggregating across years when the question asks for one year |
31.10 Practice Questions
A company's sales rose from ₹50 crores in 2020 to ₹110 crores in 2024. The percentage growth is:
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Sales of Product B over five years (in ₹ crores) are 80, 90, 95, 100, 110. The average is:
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In a pie chart of college students by stream, the angle for Science is 108°. If total students = 600, the number of Science students is:
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In the same pie chart, Arts has 144° and Engineering has 36°. The ratio of Arts to Engineering students is:
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A region's total revenue is ₹400 crores, of which Tax revenue is ₹160 crores. Tax revenue's share is:
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In a class, the weighted GPA is computed as 60 % from theory (score 80) and 40 % from practical (score 70). The weighted GPA is:
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A product's sales grew from 250 units in 2023 to 300 units in 2024. The year-on-year growth rate is:
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If a value rises by 50 % and then falls by 50 %, the net change relative to the original is:
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- Six-step approach: title → units → axes → questions → easy first → estimate.
- Key formulas: % change = (Δ/Old)×100; share = (X/Total)×100; average = sum/count; pie slice = (angle/360)×total.
- CAGR = (End/Start)^(1/n) − 1.
- Estimate before precise calculation; use round numbers to eliminate options.
- Common pitfalls: misreading units (lakh vs crore), confusing absolute vs %, using wrong base for % change.