A7 — Data interpretation: tables and charts
1. Why this topic matters here
Expect about 2.3 questions and 2.3 marks on this topic (about 3.1% of the 75 scored marks). It sits in Technical Ability, part of the 25-question aptitude block (Reasoning Ability 15 Q / 25 min + Technical Ability 10 Q / 35 min, one cut-off each). Tier 1, 1.0 hours to reach reliable recall, confidence High.
3 questions on this topic are in the observed Infosys pool (Q03, Q07), from 2 sources. They are listed in §2 and solved in ../question-banks/QB-99-OBSERVED-POOL.md.
Why the tier: expected marks per study hour, weighted by confidence, is 2.31 against a paper average of 1.84 (../data/analysis-tables.md §6). Every section has its own cut-off, so a zero here costs the whole section's chance, not only these marks. There is no calculator. Negative marking: none reported.
2. Exactly what gets asked
Three coaches independently say data interpretation is Infosys's favourite: "there is no exam of Infosys where data interpretation questions is not asked" (YT-2YHL) and "this year more DI questions are getting asked" (YT-2NTB) [REPORTED]. Data is shown as a table or as percentages that you turn into a table, then one or two computations follow.
| Sub-pattern | How it appears | Observed |
|---|---|---|
| Frequency table, "percentage less than a value" | 400 students in height groups, find the percentage shorter than 170 cm | Q03 |
| Percentage shares of a total, pass/fail and gap | Marks as % of 400, pass mark 50, find the failed subject and the best–worst difference | Q07 |
| Histogram with a pass mark | Numbers of students in score ranges, what proportion passed | discarded (X02: chart values not recoverable) |
| Bar data, growth or ratio | Output of two plants over five years | authored from the pattern |
3. Concept notes
3.1 Read the chart before you read the question
Write down: what the numbers are (units, thousands), what the total is, and what each row is a percentage of. Most DI errors are a wrong base, not wrong arithmetic.
3.2 The five calculations that cover almost everything
| Question | Formula |
|---|---|
| What percentage is A of B | A / B × 100 |
| Percentage change from old to new | (new − old) / old × 100 |
| Ratio of A to B | A : B, divide both by the HCF |
| Average | total ÷ count |
| Share of the total | part ÷ total × 100 |
3.3 Percentage charts become tables
If a pie chart says "History 13%" and the total is 400 marks, History = 13% of 400 = 52. Do this for every slice before reading the question; every answer then comes from the table.
3.4 Frequency tables
"How many are shorter than 170 cm" means the groups that end at or below 170, added up. Percentage of the class = that sum ÷ total × 100.
3.5 Approximation
With no calculator, round to round numbers and compare with the options. If options are far apart (77%, 67%, 57%), a rough figure is enough.
4. Must-memorise block
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50 | 1/8 | 12.5 |
| 1/3 | 33.3 | 1/10 | 10 |
| 1/4 | 25 | 1/12 | 8.33 |
| 1/5 | 20 | 1/16 | 6.25 |
| 1/6 | 16.7 | 1/20 | 5 |
| 1/7 | 14.3 | 3/8 | 37.5 |
Always the old value is the base for a change. Percentage points differ from percentage change.
5. Worked examples
Example 1 — frequency table (observed Q03). 400 students: 140–150 cm: 150; 150–160: 88; 160–170: 70; 170–180: 50; 180–190: 42. Shorter than 170 cm = first three groups = 150 + 88 + 70 = 308. 308 / 400 = 77%. Sanity check: 150 + 88 + 70 + 50 + 42 = 400 ✓.
Example 2 — shares of a total (observed Q07). Total 400. English 25%, Hindi 34%, Maths 18%, Science 10%, History 13%. Marks: English 100, Hindi 136, Maths 72, Science 40, History 52. Pass mark 50 → fails in Science only. Best − worst = 136 − 40 = 96. (The recalled stem says "out of 100", which Hindi's 136 contradicts; the answer holds on the chart data.)
Example 3 — quarterly sales. Sales in thousands: Q1 120, Q2 150, Q3 135, Q4 180. Total = 585.
- Growth Q1 → Q2: (150 − 120) / 120 × 100 = 25%.
- Average = 585 / 4 = 146.25.
- Share of Q4 in the year = 180 / 585 × 100 = 30.77% (4/13).
- Ratio Q4 : Q1 = 180 : 120 = 3 : 2.
Example 4 — a fall, not a rise. Output went from 730 to 560. Change = (560 − 730) / 730 = −170/730 ≈ −23.3%. The base is 730, not 560.
6. Traps and gotchas
| Trap | Why it catches people | How to avoid it |
|---|---|---|
| Wrong base for percentage change | Dividing by the new value | Always divide by the old value |
| Percentage of the wrong total | Charts have a total and a subtotal | Write "100% = …" before you start |
| Adding the wrong groups | "Shorter than 170" means up to 170 | Mark the cut-off group before adding |
| Mixing units | Thousands against units | Write the unit next to the table |
| Percentage points vs percent | 8% → 10% is +2 points but +25% | Read the question for which one is asked |
| Doing arithmetic with options far apart | Wastes time | Estimate and pick the closest option |
7. Practice questions
More questions: QB-A7-data-interpretation.md.
1. [Ratio] Study the table.
| Year | Plant A (units) | Plant B (units) |
|---|---|---|
| 2019 | 350 | 570 |
| 2020 | 760 | 400 |
| 2021 | 230 | 820 |
| 2022 | 210 | 420 |
| 2023 | 420 | 770 |
What is the ratio of Plant A's output to Plant B's output in 2021, in its simplest form? a) 19:10 b) 24:82 c) 82:23 d) 23:82
2. [Average] Study the table.
| Year | Plant A (units) | Plant B (units) |
|---|---|---|
| 2019 | 260 | 500 |
| 2020 | 330 | 640 |
| 2021 | 260 | 870 |
| 2022 | 570 | 570 |
| 2023 | 500 | 310 |
What was Plant A's average yearly output over the five years? a) 1920 b) 578 c) 384 d) 415
3. [Pie chart as a table] A student scored 400 marks in total. The share of the total earned in each subject is shown. The pass mark in each subject is 50.
| Subject | Share of total marks |
|---|---|
| Geography | 30% |
| Hindi | 25% |
| Science | 20% |
| English | 15% |
| Maths | 10% |
In which subject did the student fail, and what is the difference between the best and the worst subject scores? a) Maths, 92 b) Maths, 68 c) Maths, 80 d) Hindi, 80
4. [Frequency table] The heights of 242 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 33 |
| 150–160 | 21 |
| 160–170 | 40 |
| 170–180 | 78 |
| 180–190 | 70 |
What percentage of the students are shorter than 170 cm? a) 54.65% b) 38.84% c) 16.53% d) 61.16%
5. [Frequency table] The heights of 325 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 116 |
| 150–160 | 20 |
| 160–170 | 68 |
| 170–180 | 95 |
| 180–190 | 26 |
What percentage of the students are shorter than 180 cm? a) 29.23% b) 100% c) 92% d) 8%
6. [Frequency table] The heights of 318 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 24 |
| 150–160 | 75 |
| 160–170 | 115 |
| 170–180 | 33 |
| 180–190 | 71 |
What percentage of the students are shorter than 160 cm? a) 23.58% b) 68.87% c) 40.08% d) 31.13%
7. [Ratio] Study the table.
| Year | Plant A (units) | Plant B (units) |
|---|---|---|
| 2019 | 280 | 640 |
| 2020 | 600 | 860 |
| 2021 | 560 | 540 |
| 2022 | 760 | 710 |
| 2023 | 400 | 470 |
What is the ratio of Plant A's output to Plant B's output in 2023, in its simplest form? a) 47:40 b) 41:47 c) 76:71 d) 40:47
8. [Frequency table] The heights of 364 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 96 |
| 150–160 | 39 |
| 160–170 | 83 |
| 170–180 | 71 |
| 180–190 | 75 |
What percentage of the students are shorter than 180 cm? a) 79.4% b) 19.51% c) 20.6% d) 100%
9. [Frequency table] The heights of 386 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 22 |
| 150–160 | 113 |
| 160–170 | 80 |
| 170–180 | 102 |
| 180–190 | 69 |
What percentage of the students are shorter than 170 cm? a) 55.7% b) 67.82% c) 44.3% d) 20.73%
10. [Frequency table] The heights of 312 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 22 |
| 150–160 | 33 |
| 160–170 | 99 |
| 170–180 | 111 |
| 180–190 | 47 |
What percentage of the students are shorter than 160 cm? a) 17.63% b) 10.58% c) 20.75% d) 82.37%
11. [Frequency table] The heights of 327 students are grouped as shown.
| Height (cm) | Students |
|---|---|
| 140–150 | 81 |
| 150–160 | 66 |
| 160–170 | 116 |
| 170–180 | 23 |
| 180–190 | 41 |
What percentage of the students are shorter than 180 cm? a) 100% b) 87.46% c) 12.54% d) 7.03%
12. [Average] Study the table.
| Year | Plant A (units) | Plant B (units) |
|---|---|---|
| 2019 | 370 | 400 |
| 2020 | 610 | 330 |
| 2021 | 390 | 370 |
| 2022 | 350 | 790 |
| 2023 | 410 | 730 |
What was Plant A's average yearly output over the five years? a) 2130 b) 426 c) 440 d) 524
ANSWER KEY
- d — 230 : 820, divide both by 10 → 23:82.
- c — Total = 260 + 330 + 260 + 570 + 500 = 1920; average = 1920/5 = 384.
- c — Convert each share to marks (400 × share): Geography 120, Hindi 100, Science 80, English 60, Maths 40. Only Maths is below 50. Best − worst = 120 − 40 = 80.
- b — Students in the first 3 groups: 33 + 21 + 40 = 94. Percentage = 94/242 × 100 = 38.84%.
- c — Students in the first 4 groups: 116 + 20 + 68 + 95 = 299. Percentage = 299/325 × 100 = 92%.
- d — Students in the first 2 groups: 24 + 75 = 99. Percentage = 99/318 × 100 = 31.13%.
- d — 400 : 470, divide both by 10 → 40:47.
- a — Students in the first 4 groups: 96 + 39 + 83 + 71 = 289. Percentage = 289/364 × 100 = 79.4%.
- a — Students in the first 3 groups: 22 + 113 + 80 = 215. Percentage = 215/386 × 100 = 55.7%.
- a — Students in the first 2 groups: 22 + 33 = 55. Percentage = 55/312 × 100 = 17.63%.
- b — Students in the first 4 groups: 81 + 66 + 116 + 23 = 286. Percentage = 286/327 × 100 = 87.46%.
- b — Total = 370 + 610 + 390 + 350 + 410 = 2130; average = 2130/5 = 426.
8. Resources
- https://www.indiabix.com/data-interpretation/table-charts/ — table-chart practice in the same style as the observed items.
- https://www.indiabix.com/data-interpretation/pie-charts/ — pie charts; convert each slice to a table first.
9. Self-check
- Can you convert a pie chart to a table of marks in under a minute?
- Can you say which value is the base in "percentage change from 2020 to 2021"?
- Can you compute 77% from 308 out of 400 without a calculator?
- Can you explain percentage points against percent change with the 8% → 10% example?
- Do you estimate first when the options are far apart?
10. Sources
This file was written for this library. Infosys evidence: observed questions Q03, Q07 in ../data/questions-observed.csv; section structure and marks in ../research/03-pattern-synthesis.md §1; weightage, tier and hours in ../data/weightage.json (code A7). Confidence High. Practice questions in §7 and the bank were generated and checked by execution (brute force, simulation or inverse); see ../research/04-qa-report.md. Nothing here is a published Infosys syllabus.