Data Interpretation: Bar Graphs and Line Graphs
Data Interpretation: Bar Graphs and Line Graphs
A bar graph compares categories side by side; a line graph shows how a quantity changes over time. In the exam you read the values off the graph, so first write them down as a small table; every question then becomes table arithmetic. Here the graph values are given as tables.
1. Reading Rules
| Graph | What to read | Typical question |
|---|---|---|
| Simple bar | One value per category | Highest, lowest, difference, percentage more |
| Multiple bar | Two or more bars per category | Largest gap, ratio of totals, share of one group |
| Line graph | Values at time points | Growth or fall %, steepest rise, average |
| Two-line graph | Two series on the same axes | Years where one exceeds the other, gap, ratio |
Steepest line segment = largest absolute change; it is not always the largest percentage change
Percentage change between two points = (later − earlier)/earlier × 100
✗ The steepest rise on the line graph is always the highest growth rate | ✓ Divide by the starting value: the 14-point rise of 2025 (70 to 84, 20%) is steeper than the 10-point rise of 2020 (40 to 50, 25%) but slower in percentage terms
✗ Read the bar heights as exact | ✓ Use the scale and the gridlines, and pick the nearest option when values are approximate
हिंदी नोट: दंड आलेख में श्रेणियों की तुलना होती है और रेखा आलेख में समय के साथ बदलाव। पहले आलेख के मान एक छोटी तालिका में लिख लीजिए, फिर प्रतिशत और अनुपात निकालिए।
Exam Pointer: Verified NTPC pattern: a multiple bar graph of male and female employees in several companies, asking for the largest difference (January 2021 CBT-1). Line-graph questions had no verified NTPC shift in our check and are tagged syllabus-based.
2. Data Sets
Bar graph values: employees in five companies.
| Company | A | B | C | D | E |
|---|---|---|---|---|---|
| Male | 450 | 380 | 520 | 300 | 410 |
| Female | 300 | 420 | 360 | 280 | 270 |
Line graph values: sales of a firm (₹ crore).
| Year | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 |
|---|---|---|---|---|---|---|---|
| Sales | 40 | 50 | 45 | 60 | 75 | 70 | 84 |
Two-line graph values: exports and imports of a country (₹ thousand crore).
| Year | 2021 | 2022 | 2023 | 2024 | 2025 |
|---|---|---|---|---|---|
| Exports | 120 | 150 | 140 | 180 | 210 |
| Imports | 100 | 160 | 150 | 170 | 200 |
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Multiple bar graph: largest difference and shares
[PYQ: NTPC CBT-1 4-Jan-2021 Shift-2]
EXAM LEVEL
Q. From the employee bar graph, which company has the largest difference between male and female employees?
Differences: A 150, B 40, C 160, D 20, E 140. The largest is C.
Answer: Company C (160)
EXAMATLAS LEVEL
Q. From the employee bar graph, in which company do women form the largest share, and what is the ratio of total male to total female employees?
Female shares: A 300/750 = 40%, B 420/800 = 52.5%, C 360/880 ≈ 40.9%, D 280/580 ≈ 48.3%, E 270/680 ≈ 39.7%, so B. Males total 2,060 and females 1,630, a ratio of 206 : 163.
Answer: Company B; 206 : 163
Pattern 2: Bar graph: percentage more and comparison with the average
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. From the employee bar graph, the male employees of C are what percentage more than those of D?
(520 − 300)/300 × 100 = 220/3 ≈ 73.33%.
Answer: About 73.33%
EXAMATLAS LEVEL
Q. From the employee bar graph, find the average number of female employees per company and the number of companies above that average.
1,630/5 = 326. B (420) and C (360) are above it.
Answer: 326; 2 companies
Pattern 3: Line graph: growth and fall
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. From the sales line graph, find the percentage increase in sales from 2021 to 2022.
(60 − 45)/45 × 100 = 33.33%.
Answer: 33.33%
EXAMATLAS LEVEL
Q. From the sales line graph, in which year was the percentage growth over the previous year highest, and in which year was the percentage fall largest?
Rises: 2020 25%, 2022 33.3%, 2023 25%, 2025 20%. Falls: 2021 10%, 2024 about 6.7%. Highest growth 2022; largest fall 2021.
Answer: 2022; 2021
Pattern 4: Two-line graph: comparing two series
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. From the exports-imports graph, in which years did exports exceed imports?
2021 (120 > 100), 2024 (180 > 170) and 2025 (210 > 200).
Answer: 2021, 2024, 2025
EXAMATLAS LEVEL
Q. From the exports-imports graph, find the difference between average exports and average imports, and the year in which the ratio of exports to imports was highest.
Exports total 800 (average 160) and imports total 780 (average 156), a difference of 4. Ratios above 1: 2021 1.2, 2024 about 1.06, 2025 1.05. Highest in 2021.
Answer: 4 (₹ thousand crore); 2021
60-Second Revision
- Turn the graph into a table first.
- Multiple bars: compute each gap or share, then compare.
- Line graph growth: divide by the earlier value.
- Two lines: compare year by year; averages from column totals.