Data Interpretation Concepts and Worked Examples

Campus aptitude tests from TCS NQT to analytics-firm assessments all include data interpretation, and the same five techniques handle every question type across pie charts, bar graphs, line graphs, tables, and text-based caselets.

The TCS National Qualifier Test includes DI as part of its Numerical Ability section. Infosys InfyTQ and Wipro’s online assessments include similar sets. The question count per test varies, but the data types are consistent. This article works through one full 4-question example per type, with every calculation re-derived from the raw numbers.

Reading DI Data: What Changes by Chart Type

Before any calculation, spend 15 to 20 seconds reading the chart. The key details are: what the data represents, what the unit is, and what time period or category split is shown. Missing a unit (lakhs vs. crores, hundreds vs. thousands) is the most common source of wrong answers that have nothing to do with arithmetic.

The table below maps each chart type to what it typically represents and what kinds of questions follow.

Chart Type	What it shows	Common question types
Pie chart	Share or proportion of a whole	Value from percentage, ratio between slices, new percentage after adding data
Bar graph	Quantities across categories or years	Largest or smallest, percentage change, year-over-year difference, average
Line graph	Trends over time	Crossover point, rate of change, total across periods, projection
Table	Multi-variable comparison	Row or column totals, conditional counts, ratio between cells
Caselet	Text-embedded multi-variable data	Multi-step chained calculations, percentage vs. percentage-point

The fraction and percentage arithmetic in Time and Work aptitude questions follows the same structure as DI percentage calculations: express a part as a fraction of the whole, convert to percentage, and verify that the denominator is the right reference value.

Pie Charts: Worked Example

A company’s job applications are split across five engineering branches. The table below gives the distribution by branch and count.

Branch	Share	Count
CSE	35%	840
ECE	25%	600
Mech	20%	480
IT	12%	288
Others	8%	192
Total	100%	2,400

• Q1: How many applications came from CSE?

• Step: 35% of 2,400 = 0.35 × 2,400 = 840 applications.

• Q2: How many more applications came from ECE than from IT?

• Step: ECE = 25% × 2,400 = 600. IT = 12% × 2,400 = 288. Difference = 600 - 288 = 312 applications.

• Q3: What percentage of non-CSE applications came from Mech?

• Step: Non-CSE = (100 - 35)% × 2,400 = 65% × 2,400 = 1,560. Mech = 20% × 2,400 = 480. Mech share of non-CSE = 480 / 1,560 × 100 = 30.8%.

• Q4: If 200 additional applications arrive, all from ECE, what is ECE’s new percentage share?

• Step: New total = 2,400 + 200 = 2,600. New ECE count = 600 + 200 = 800. New share = 800 / 2,600 × 100 = 30.8%.

• Tip: Q3 and Q4 happen to return the same percentage value here. That is a coincidence of these specific numbers, not a general rule. Always re-derive rather than copying an earlier answer.

Bar Graphs: Worked Example

A bar chart shows production output (in units) for two factories across four years.

Year	Factory A	Factory B
2020	3,600	2,800
2021	4,200	3,500
2022	3,800	4,000
2023	5,000	4,400

• Q1: In which year did Factory B first exceed Factory A?

• Step: 2020: A=3,600, B=2,800 (A higher). 2021: A=4,200, B=3,500 (A higher). 2022: A=3,800, B=4,000 (B higher). Answer: 2022.

• Q2: By what percentage did Factory A’s output grow from 2020 to 2023?

• Step: Increase = 5,000 - 3,600 = 1,400. Percentage = 1,400 / 3,600 × 100 = 38.9%.

• Q3: What was the average combined output (A + B) per year across all four years?

• Step: Combined totals: 2020 = 6,400; 2021 = 7,700; 2022 = 7,800; 2023 = 9,400. Sum = 31,300. Average = 31,300 / 4 = 7,825 units per year.

• Q4: In 2023, what percentage of the total combined output came from Factory B?

• Step: 2023 combined = 5,000 + 4,400 = 9,400. Factory B = 4,400. Share = 4,400 / 9,400 × 100 = 46.8%.

Line Graphs: Worked Example

A line graph shows quarterly revenue (in crore) for two product lines across four quarters.

Quarter	Product X	Product Y
Q1	12	8
Q2	15	14
Q3	11	16
Q4	18	15

• Q1: In which quarter did Product Y first exceed Product X?

• Step: Q1: X=12, Y=8 (X higher). Q2: X=15, Y=14 (X higher). Q3: X=11, Y=16 (Y higher). Answer: Q3.

• Q2: What was the total combined revenue across all eight data points?

• Step: X total = 12 + 15 + 11 + 18 = 56. Y total = 8 + 14 + 16 + 15 = 53. Combined = 109 crore.

• Q3: By what percentage did Product X revenue change from Q1 to Q4?

• Step: Increase = 18 - 12 = 6. Percentage = 6 / 12 × 100 = 50% increase.

• Q4: In which quarter was combined revenue (X + Y) the highest?

• Step: Q1 = 20; Q2 = 29; Q3 = 27; Q4 = 33. Answer: Q4 (33 crore).

Tables: Worked Example

A table shows units sold (in hundreds) by five salespeople across three product categories.

Salesperson	Phones	Tablets	Laptops
Arjun	14	8	6
Bala	10	12	9
Chitra	18	7	11
Dinesh	8	15	7
Ezhil	12	10	13

• Q1: Which salesperson had the highest total sales?

• Step: Arjun = 14+8+6 = 28; Bala = 10+12+9 = 31; Chitra = 18+7+11 = 36; Dinesh = 8+15+7 = 30; Ezhil = 12+10+13 = 35. Answer: Chitra (3,600 units).

• Q2: What is the average number of Tablet units sold across all five salespeople?

• Step: Tablet column sum = 8+12+7+15+10 = 52. Average = 52 / 5 = 10.4 (hundreds) = 1,040 units.

• Q3: What percentage of total Laptop sales did Ezhil account for?

• Step: Total Laptops = 6+9+11+7+13 = 46. Ezhil = 13. Share = 13 / 46 × 100 = 28.3%.

• Q4: How many salespeople sold more Phones than Tablets?

• Step: Arjun 14 vs 8 (yes); Bala 10 vs 12 (no); Chitra 18 vs 7 (yes); Dinesh 8 vs 15 (no); Ezhil 12 vs 10 (yes). Answer: 3 salespeople.

Caselets and Mixed DI Sets

A caselet gives you the same data as a table but writes it into paragraph form. The approach: read the entire paragraph first, extract the numbers into a quick grid on paper, then treat it as a standard DI set. Skipping the extraction step and working from the paragraph directly is where chained errors enter.

Analytics-firm recruitment rounds from Mu Sigma MuApt questions to the ZS Associates aptitude test rely heavily on caselets and mixed DI formats. The IndiaBix DI practice section has categorised sets for each type.

The data below represents employee expense claims over three months. In an actual test caselet, this data appears embedded in a paragraph rather than as a table; the first step is always to extract it into a grid like this.

Month	Claims filed	Amount (lakh)	Reimbursed in full
January	120	18	40%
February	95	14.25	60%
March	140	21	50%

• Q1: How many claims were reimbursed in full across all three months?

• Step: January: 40% × 120 = 48. February: 60% × 95 = 57. March: 50% × 140 = 70. Total = 48 + 57 + 70 = 175 claims.

• Q2: What was the average value per claim in February?

• Step: 14.25 lakh / 95 = 0.15 lakh per claim = 15,000 per claim.

• Q3: What percentage of total claims across the three months were filed in March?

• Step: Total = 120 + 95 + 140 = 355. March = 140. Share = 140 / 355 × 100 = 39.4%.

• Q4: What was the total amount reimbursed in full across all three months?

• Step: January: 40% × 18 = 7.2 lakh. February: 60% × 14.25 = 8.55 lakh. March: 50% × 21 = 10.5 lakh. Total = 7.2 + 8.55 + 10.5 = 26.25 lakh.

Percentage of Total vs. Percentage-Point Change

This is the most frequently confused pair in multi-part DI sets, especially caselets.

• Percentage of total: a share expressed as a fraction of the whole. In the caselet above, March’s 140 claims represent 39.4% of the 355 total.
• Percentage-point change: the arithmetic difference between two percentage figures.
• Example: If a department’s share rose from 30% to 45%, it increased by 15 percentage points, not 50%. The figure 50% is the relative increase (15/30 × 100) and answers a different question.

The error shows up in questions phrased as “by how much did the share increase?” Read the phrasing carefully before calculating.

In chained DI sets, where Q2 uses the output of Q1, re-derive from the source table for each question. A wrong Q1 answer cascades into Q2, Q3, and Q4 if you carry it forward.

The same precision about what a number actually measures transfers directly to reading AI model evaluation reports, where a result labelled “improved by X percentage points” means something very different from “improved by X percent.” TinkerLLM at ₹299 is a hands-on environment where you can run live experiments against real language models and interpret those benchmark numbers yourself, applying the same careful numeracy DI prep builds.