Data Analysis and Interpretation: Mains-Level Sets

This chapter answers the Data Analysis and Interpretation (DI) part of the quantitative and DI papers of IBPS Clerk, SBI Clerk, IBPS PO, SBI PO and IBPS RRB. The Mains versions of these papers use sets of about five questions on one dataset, with heavy calculation under a tight sectional clock, so the skill tested is choosing what to compute and what to skip. The chapter teaches a fixed reading routine for every set, then the tools for each dataset type: tables and missing-data tables, bar, line and pie charts, radar charts and two- or three-chart sets, caselets, and data sufficiency with three statements. The traps are the same in every format: percentage versus percentage points, the base of a percentage, and exact versus approximate calculation. In the practice questions every dataset is written out in the question, in text form, because the app shuffles questions.

The Set Routine and the Three Traps

Spend the first 30 seconds on the data, not on the first question. Read the title and units (₹ crore or ₹ lakh, thousands or units, percent or number), read the row and column labels, and note what is given as a percentage and what as a count. Then read all five questions and do the easy ones first: a direct lookup, a sum or a simple ratio takes 20 seconds, and the set is scored the same whichever order you answer in. Leave the one question that needs a long chain for the end.

Three traps appear in almost every set. Trap 1, base. A percentage is always of some base: "B is what percent more than A" uses A as the base, "A is what percent less than B" uses B. Trap 2, percentage points. When a rate moves from 60% to 75% the rise is 15 percentage points but a 25% rise (15 ÷ 60). Trap 3, absolute versus relative. The year with the largest rupee increase need not be the year with the largest percentage increase, because the base is different each year.

Four formulas that cover most DI questions
QuantityFormulaWorked example
Percentage change(new − old) ÷ old × 100240 to 300: 60 ÷ 240 = 25%
Percentage pointsnew rate − old rate60% to 75%: 15 points
Two successive changesa + b + ab ÷ 100+20% then −20%: 20 − 20 − 4 = −4%
Averagesum ÷ count40, 45, 50, 60, 55: 250 ÷ 5 = 50
⚠️ Exam trap
A rise of 20% followed by a fall of 20% does not return to the start. Take 100: it becomes 120, then 20% of 120 is 24, giving 96. The fall is taken on the larger number, so the net result is a 4% loss. Options that say "unchanged" are the trap.

Tables and Missing-Data Tables

A table is the safest format: every number is exact, so scan for the quantity each question needs and compute nothing else. For percentage questions, rewrite the ratio in simplest form first: 300 out of 240 becomes 5 : 4, which is 125% at sight. Learn the common fraction values (1/8 = 12.5%, 1/6 = 16.67%, 1/7 = 14.29%, 1/9 = 11.11%) so that you convert without dividing.

In a missing-data table some cells are blank or marked "?" and must be rebuilt from percentages, ratios or totals given in the same table. Work in this order: fill every cell that can be found from one relation, then use the cells you have just filled. Example: a bank shows three branches. Branch A has deposits ₹500 crore and a credit-deposit (CD) ratio of 60%, where CD ratio = loans ÷ deposits × 100; Branch B has loans ₹360 crore and CD ratio 80%; Branch C has deposits ₹400 crore and loans ₹280 crore. Then A's loans = 60% of 500 = ₹300 crore, and B's deposits = 360 ÷ 0.8 = ₹450 crore. The three branches together hold deposits of ₹1,350 crore and loans of ₹940 crore.

🧠 Memory trick
To go backwards from a final figure, divide by the multiplier rather than guessing the percentage. If a town grew 20% and then 25% to reach 1,20,000, divide by 1.25 to get 96,000, then by 1.2 to get 80,000. Adding the two percentages (45%) and taking 45% off is wrong, because each rise had a different base.
🎯 Why it matters
Missing-data sets are built so that one cell is reachable from a direct relation. If you are stuck, you have probably missed a row total, a column total or a percentage that links two blanks.

Bar, Line and Pie Charts

In a bar or line graph the question gives you readings, so read the two or three values you need and ignore the rest. Example: Company A produced 40, 45, 50, 60 and 55 thousand units in five years and Company B produced 30, 48, 40, 50 and 62 thousand. A's total is 250 and B's is 230, so B's total as a percent of A's is 230 ÷ 250 = 92%. For line graphs, a steeper segment means a larger change, but compare percentage change only after reading the starting value.

In a pie chart the whole circle is 100% = 360°, so 1% = 3.6°. A sector of 54° is 54 ÷ 3.6 = 15%. Pie charts give shares, not amounts: you need one real amount to unlock the rest. If a family spends 30% of its income on food and food costs ₹18,000, the income is 18,000 ÷ 0.30 = ₹60,000; savings of 20% are ₹12,000 and education of 15% is ₹9,000, a gap of ₹3,000. If angles are given instead, the unit is the amount per degree: a 54° sector of ₹2.7 lakh gives ₹0.05 lakh per degree, so a 144° sector is ₹7.2 lakh.

Largest rupee rise is 2024; largest percentage rise is 2022
YearSales (₹ lakh)Increase% increase
2021240––
20223006025%
20233303010%
20243966620%
⚠️ Exam trap
For "which year had the highest growth" always say which kind. In the table, 2024 adds the most rupees (66 lakh) but 2022 has the highest percentage growth (25%) because its base was only 240. Questions that say "growth" or "rise in percent" want 2022.

Radar Charts and Two- or Three-Chart Sets

A radar (web) chart plots several categories on spokes from a centre, with one polygon per series. It is only a table in disguise: each spoke is one row and each polygon is one column. In the exam read the values off the spokes into a small two-line table before answering. Example: Riya scores 80, 60, 90, 50, 70, 50 and Sana scores 70, 75, 85, 65, 60, 85 in six subjects. Sana beats Riya in three subjects (the second, fourth and sixth); the totals are 400 and 440, so Sana's total is 40 ÷ 400 = 10% more.

In a two- or three-chart set each chart carries a different part of the information, and questions join them. Example: a table gives candidates for exams P, Q and R as 80, 60 and 40 thousand, and a second chart gives the percentage of women as 35%, 50% and 60%. Women are 28 + 30 + 24 = 82 thousand, so men are 180 − 82 = 98 thousand. Write the join once (here, a women column) and reuse it for every question.

🧠 Memory trick
Compare before you compute. A table with 5% of 1,200, 4% of 1,500 and 7.5% of 800 looks as if the 7.5% plant must have the most defects. But 60, 60 and 60 are the three counts: a higher rate on a smaller base can give the same number. Always multiply rate by base before ranking.

Caselets: Turning Words into a Table

A caselet is a short paragraph of numbers and relations with no chart. The method is to name the unknown, write every sentence as an equation or a table cell, and solve. Example: 60 officers work in Loans, Deposits and Forex. Loans has 25% more officers than Forex and Deposits has 10 fewer than Loans. Let Forex = f; then Loans = 1.25f, Deposits = 1.25f − 10, and 3.5f − 10 = 60, so f = 20. Loans has 25 and Deposits has 15, so Deposits is 15 ÷ 25 = 60% of Loans.

Overlap caselets use two sets: at least one = A + B − both. In a survey of 200 customers, 120 use mobile banking, 90 use net banking and 30 use neither. At least one means 170, so both = 120 + 90 − 170 = 40, and only net banking = 90 − 40 = 50. Draw the two circles with the "both" region first, then fill the "only" regions by subtraction.

⚠️ Exam trap
"More than" and "less than" statements flip the base. "Deposits has 10 fewer than Loans" is Loans − 10, not 10% less. Read the unit after the number before writing the equation.

Data Sufficiency with Three Statements

In data sufficiency you are never asked for the answer, only whether the answer can be found. With three statements P, Q and R the question becomes: which statements, alone or in pairs, are enough? Test each statement alone, then each pair, and stop as soon as you know. Do not calculate the final value; only check that every unknown needed is fixed.

Example: find the speed of a boat in still water. P: downstream speed 14 km/h. Q: upstream speed 8 km/h. R: stream speed 3 km/h. Still-water speed = (downstream + upstream) ÷ 2 = downstream − stream = upstream + stream. P and Q give 11, P and R give 11, Q and R give 11, but no single statement is enough. So any two statements suffice.

⚠️ Exam trap
Check that statements do not secretly depend on each other. For profit percent, selling price ₹1,150 (P) is useless without cost price ₹1,000 (Q); a marked price of ₹1,250 with an 8% discount (R) gives the same selling price ₹1,150 but still no cost. So Q must be used with either P or R, and neither P with R nor any single statement is enough.
🎯 Why it matters
If an "any two" answer is correct, an option saying "only P and Q" is wrong, because it denies that the other pairs work. Read "only" as a claim about every other pair.

Key takeaways

  • Spend 30 seconds on units, labels and which values are percentages; answer the quick lookups first and leave the long chain for last.
  • A percentage always has a base. Percentage points are a difference of rates; percentage change is the difference divided by the old rate.
  • The largest rupee rise and the largest percentage rise usually fall in different years; +20% then −20% is a 4% loss, not zero.
  • Pie chart: 1% = 3.6°. Shares need one real amount to turn into rupees. A radar chart is a table in disguise.
  • Rate × base before ranking: a higher rate on a smaller base can give the same count. Go backwards by dividing by the multiplier.
  • Caselets: name the unknown and write each sentence as an equation. Data sufficiency: test each statement, then each pair, and do not compute the final value.

Practice questions (18)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. A firm's sales (₹ lakh) were: 2021, 240; 2022, 300; 2023, 330; 2024, 396. In which year was the percentage growth over the previous year the highest?

    1. 2024
    2. 2023
    3. 2022
    4. All three years are equal
    Show answer

    Answer: C — 2022

    Growth is 60/240 = 25% in 2022, 30/300 = 10% in 2023 and 66/330 = 20% in 2024. The tempting answer is 2024, which has the largest rupee increase (66 lakh), but the question asks for percentage growth, whose base differs each year.

  2. A school's pass percentage rose from 60% to 75%. By what percent did the pass percentage increase?

    1. 25%
    2. 15%
    3. 20%
    4. 40%
    Show answer

    Answer: A — 25%

    The rise is 15 percentage points, and the percentage increase is 15 ÷ 60 × 100 = 25%. The option 15% is tempting because it confuses percentage points with percent change; the base of the increase is the old rate, 60.

  3. A pie chart shows a family's monthly spending: Rent 25%, Food 30%, Education 15%, Savings 20%, Others 10%. If the family spends ₹18,000 on Food, how much more is saved than is spent on Education?

    1. ₹2,000
    2. ₹3,000
    3. ₹5,000
    4. ₹6,000
    Show answer

    Answer: B — ₹3,000

    Food is 30% = ₹18,000, so the total is ₹60,000. Savings are 20% = ₹12,000 and Education 15% = ₹9,000, a gap of ₹3,000 (5% of 60,000). ₹5,000 comes from reading the gap 5% as 5 thousand without finding the base.

  4. A bar graph gives production (thousand units) of Company A over five years as 40, 45, 50, 60 and 55, and of Company B as 30, 48, 40, 50 and 62. The total production of B is what percent of the total production of A?

    1. 108.7%
    2. 88%
    3. 96%
    4. 92%
    Show answer

    Answer: D — 92%

    A's total is 250 and B's total is 230, so B is 230 ÷ 250 × 100 = 92% of A. The value 108.7% is the reverse ratio, 250 ÷ 230, which answers 'A is what percent of B'.

  5. A line graph gives the profit (₹ crore) of Company P over four years as 80, 100, 120 and 90, and of Company Q over the same years as 60, 90, 105 and 135. In the fourth year, Q's profit is what percent more than P's profit?

    1. 50%
    2. 33.33%
    3. 45%
    4. 66.67%
    Show answer

    Answer: A — 50%

    In the fourth year Q = 135 and P = 90, so the excess is 45 and, with P as the base, 45 ÷ 90 = 50%. The figure 33.33% uses Q as the base (45 ÷ 135), which would answer 'P is what percent less than Q'.

  6. A bank's three branches have: Branch A, deposits ₹500 crore, loans '?', credit-deposit ratio 60%; Branch B, deposits '?', loans ₹360 crore, credit-deposit ratio 80%; Branch C, deposits ₹400 crore, loans ₹280 crore. (Credit-deposit ratio = loans ÷ deposits × 100.) By how much do the total deposits of the three branches exceed their total loans?

    1. ₹360 crore
    2. ₹450 crore
    3. ₹410 crore
    4. ₹320 crore
    Show answer

    Answer: C — ₹410 crore

    A's loans = 60% of 500 = 300; B's deposits = 360 ÷ 0.8 = 450. Deposits total 500 + 450 + 400 = 1,350 and loans total 300 + 360 + 280 = 940, so the excess is ₹410 crore. Multiplying 360 by 0.8 instead of dividing gives 288, which is the tempting error.

  7. A radar chart gives the marks of Riya in six subjects (Maths, English, Reasoning, General Awareness, Computer, Banking) as 80, 60, 90, 50, 70, 50 and of Sana in the same order as 70, 75, 85, 65, 60, 85. In how many subjects did Sana score more than Riya?

    1. 2
    2. 3
    3. 4
    4. 5
    Show answer

    Answer: B — 3

    Compare subject by subject: English 75 > 60, General Awareness 65 > 50 and Banking 85 > 50 favour Sana, while Maths, Reasoning and Computer favour Riya. So the count is 3. Choosing 4 comes from also counting the close Reasoning pair (85 against 90), which Riya wins.

  8. Riya's marks in six subjects are 80, 60, 90, 50, 70 and 50, and Sana's marks in the same six subjects are 70, 75, 85, 65, 60 and 85. Sana's total marks are what percent more than Riya's total marks?

    1. 10%
    2. 9.09%
    3. 8%
    4. 12.5%
    Show answer

    Answer: A — 10%

    Riya's total is 400 and Sana's is 440, so the excess is 40 and 40 ÷ 400 = 10% with Riya's total as the base. The value 9.09% divides by Sana's total (40 ÷ 440), which would answer 'Riya's total is what percent less than Sana's'.

  9. Candidates appearing (in thousands) in three exams are: P, 80; Q, 60; R, 40. The percentage of women among them is: P, 35%; Q, 50%; R, 60%. How many men appeared in the three exams together?

    1. 82 thousand
    2. 90 thousand
    3. 102 thousand
    4. 98 thousand
    Show answer

    Answer: D — 98 thousand

    Women are 35% of 80 = 28, 50% of 60 = 30 and 60% of 40 = 24, a total of 82 thousand. Men are 180 − 82 = 98 thousand. The option 82 thousand is the women's total, which answers a different question.

  10. A pie chart of a company's yearly budget shows central angles: Salaries 144°, Rent 72°, Marketing 54°, Miscellaneous 90°. If Marketing costs ₹2.7 lakh, how much is spent on Salaries?

    1. ₹7.2 lakh
    2. ₹6.4 lakh
    3. ₹8.1 lakh
    4. ₹5.4 lakh
    Show answer

    Answer: A — ₹7.2 lakh

    Marketing 54° = ₹2.7 lakh, so each degree is ₹0.05 lakh and Salaries 144° = 144 × 0.05 = ₹7.2 lakh. The option ₹6.4 lakh is wrong: the angle is a share of 360°, so the unit is the amount per degree, 2.7 ÷ 54, and every sector is its angle times that unit.

  11. The population of a town in 2022 is 1,20,000. It rose by 25% from 2021 to 2022 and by 20% from 2020 to 2021. What was its population in 2020?

    1. 82,759
    2. 66,000
    3. 80,000
    4. 96,000
    Show answer

    Answer: C — 80,000

    Go backwards by dividing: 1,20,000 ÷ 1.25 = 96,000 in 2021, then 96,000 ÷ 1.2 = 80,000 in 2020. Subtracting 45% (the sum of 20% and 25%) gives 66,000, which is wrong because each percentage has a different base; 96,000 is only the 2021 figure.

  12. The revenue index of a company was 100 in 2022. It rose by 20% in 2023 over 2022, and then fell by 20% in 2024 from the 2023 level. How does the 2024 revenue compare with 2022?

    1. The same
    2. 4% higher
    3. 2% lower
    4. 4% lower
    Show answer

    Answer: D — 4% lower

    2023 = 120 and 2024 = 120 − 24 = 96, which is 4% below 100. The answer 'the same' is the trap: the 20% fall is taken on the larger figure 120, not on 100.

  13. A bank has 60 officers in three sections: Loans, Deposits and Forex. Loans has 25% more officers than Forex, and Deposits has 10 fewer officers than Loans. The number of officers in Deposits is what percent of the number in Loans?

    1. 40%
    2. 60%
    3. 75%
    4. 80%
    Show answer

    Answer: B — 60%

    Let Forex = f, Loans = 1.25f and Deposits = 1.25f − 10. The total 3.5f − 10 = 60 gives f = 20, so Loans = 25 and Deposits = 15, and 15 ÷ 25 = 60%. Using 15 ÷ 60 = 25% or 10 ÷ 25 = 40% answers a different question.

  14. Of 200 customers surveyed, 120 use mobile banking, 90 use net banking and 30 use neither. How many customers use only net banking?

    1. 50
    2. 40
    3. 60
    4. 30
    Show answer

    Answer: A — 50

    At least one service is used by 200 − 30 = 170, so both = 120 + 90 − 170 = 40 and only net banking = 90 − 40 = 50. The value 40 is the 'both' region, and 60 forgets that the 90 net-banking users include those who also use mobile banking.

  15. Question: What is the speed of a boat in still water? P: The downstream speed is 14 km/h. Q: The upstream speed is 8 km/h. R: The speed of the stream is 3 km/h. Which of the following is correct?

    1. Only P and Q together are sufficient, and the other pairs are not
    2. All three statements are needed together to find the speed
    3. Statement P alone is sufficient to find the speed
    4. Any two of the three statements are sufficient, but no single statement is
    Show answer

    Answer: D — Any two of the three statements are sufficient, but no single statement is

    Still-water speed is (downstream + upstream) ÷ 2, downstream − stream, or upstream + stream. So P with Q gives 11, P with R gives 11, and Q with R gives 11; each statement alone gives only one of the two needed values. 'Only P and Q' is wrong because it denies that the other pairs also work.

  16. Question: What is the profit percent on an article? P: Its selling price is ₹1,150. Q: Its cost price is ₹1,000. R: Its marked price is ₹1,250 and it was sold at an 8% discount. Which combination of statements is sufficient?

    1. P and R together, without Q
    2. Q together with either P or R
    3. P alone, because it gives the selling price
    4. R alone, because it gives marked price and discount
    Show answer

    Answer: B — Q together with either P or R

    Profit percent needs both cost price and selling price. Q gives the cost price; P gives the selling price directly and R gives the same ₹1,150 (1,250 × 0.92). So Q with P or Q with R works, and gives 15%. P with R only repeats the selling price and still has no cost price.

  17. A table shows three plants: X produces 1,200 units with 5% defective; Y produces 1,500 units with 4% defective; Z produces 800 units with 7.5% defective. P: All three plants have the same number of defective units. Q: Z has the most defective units because it has the highest defect rate. R: Y has the fewest defective units because it has the lowest defect rate. Which statement(s) is/are correct?

    1. Q only
    2. R only
    3. P only
    4. Q and R only
    Show answer

    Answer: C — P only

    Defective units are 5% of 1,200 = 60, 4% of 1,500 = 60 and 7.5% of 800 = 60, so only P is true. Q and R both rank plants by rate alone, which is wrong because the production base differs in each plant.

  18. A company's revenue was ₹4,812 crore in 2023 and ₹5,397 crore in 2024. To the nearest whole number, the percentage growth in revenue is closest to which of the following?

    1. 12%
    2. 10%
    3. 15%
    4. 8%
    Show answer

    Answer: A — 12%

    The rise is 5,397 − 4,812 = 585, and 585 ÷ 4,812 is about 12.2%, so the nearest value is 12%. Quick check: 4,812 is about 4,800, and 12% of 4,800 is 576. Using 5,397 as the base gives about 10.8%, which is the tempting wrong base.