Quant · Data interpretation
Data interpretation (DI) means reading numbers off a table, bar graph, line graph or pie chart and answering a few questions about them. Reading tables and charts: totals, percentage change, pie-chart angles and shares, row averages, weighted averages and successive growth. DI rewards calm reading more than calculation — every question is one fraction or one product away, and the data is given in clean, round numbers by design. Tier 2 sets often attach a 5-question block to one table, so per-table setup pays twice. Our topic notes put DI at about 2 questions in a Tier 1 paper and about 5 in Tier 2, so it is a smaller block than Percentage or Algebra, but it is among the most predictable.
The good news is that DI needs very few formulas. Almost everything is a total, an average, a ratio, a percentage or a percentage change. What decides your score is reading the question carefully (which row, which year, which unit, percent of what) and keeping the arithmetic light. The sections below give you the formulas from our notes, a method for each chart type, the traps that cost marks, and the calculation habits that save time. Jump straight to what you need.
Grouped by the kind of question they answer. Each group links to its full subtopic page with notes, question types and practice.
A data table gives values for rows (plants, cities, shops) across columns (usually years). Read the row and column the question names, then do one small sum: a total, an average, a ratio or a count. Nothing more.
Percentage questions on data compare one value with another: a rise, a share, or a gap in points. The base is everything. Ask first: percent of what? The number after 'of' is the base you divide by.
Base = the old / original value.
A pie chart splits a total into slices by angle: 360 degrees is the whole, so 1 degree is total ÷ 360. Two conversions answer everything: degrees to percent (360° = 100\%) and degrees to value (1° = total ÷ 360).
theta is the slice angle in degrees.
Table averages rebuild the total first: average = total ÷ count. Rows can carry their own counts (workers per salary band, machines per output), so weighted averages, not plain ones, are the default here.
n_i is the count in each band or row.
Growth questions track a value rising year after year: one year's rate, the total rate over several years, or the starting value when only the end is known. Every version still rests on one line: new value = old value \times growth multiplier.
Every percentage question reduces to part ÷ whole × 100 or change ÷ original × 100. If you can name the part and the whole, or the change and the original, before you start computing, you will rarely pick the wrong formula.
Read the title and the unit line first (thousands, lakhs, crores, percent), then the row and column headings. Most questions touch one row or one column, so add or compare only that strip and ignore the rest. For count-style questions (how many years was a value above a figure) sweep the strip once and tick as you go. Questions that use several columns at once often reward writing a small helper row, such as a total or a ratio, once and reusing it.
A bar graph is a table drawn as bars, so first turn the bars you need into numbers and jot them down. Check the axis scale and where it starts before you compare heights by eye; a bar that looks twice as tall may not be twice the value. With grouped or stacked bars, read the legend to know which colour is which series, and remember that in a stacked bar a segment's value is its own length, not the top of the stack.
Line graphs are about change over time, so most questions ask for a rise, a fall or a percentage change between two points. Read the two values off the axis, then use change ÷ original × 100 with the earlier value as the original. For "in which year was the increase highest" questions, compare the differences between neighbouring points. The steepest segment is a good first guess, but confirm with numbers when percent change is asked, because the largest absolute rise is not always the largest percentage rise.
A pie divides a total into slices measured in degrees or percentages. With degrees, 360° is the whole, so value = angle ÷ 360 × total and percent = angle ÷ 3.6. If only one slice has a known value, find the value of 1° (or 1%) once and price every other slice from it. When two pies are compared, convert each slice to an actual value using its own pie's total before comparing; equal percentages on pies with different totals are not equal amounts.
A caselet gives the data in a paragraph, and a mixed set combines, say, a table and a pie. Do not start answering. Spend a minute converting the caselet into a small table with labelled rows and columns, filling the unknowns from the given ratios or totals. For mixed sets, work out which chart gives the total and which gives the split, then connect them. The setup time is repaid across the several questions that follow the same data.
One worked set for each chart type. Read the chart, try each question yourself, then tap Show answer to see the answer and the shortcut. Every figure, answer and solution below is computed from the same data, so they always agree.
| Plant | 2020 | 2021 | 2022 | 2023 | 2024 |
|---|---|---|---|---|---|
| Plant A | 40 | 55 | 45 | 60 | 70 |
| Plant B | 50 | 45 | 60 | 55 | 65 |
| Plant C | 30 | 35 | 50 | 45 | 55 |
Q1. What was the total production of all three plants together in 2023?
Q2. By what percentage did Plant A's production rise from 2020 to 2024?
Q3. What was Plant C's average annual production over the five years?
| Series | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
|---|---|---|---|---|---|---|
| Revenue | 120 | 135 | 128 | 150 | 165 | 180 |
| Expenditure | 90 | 100 | 110 | 115 | 125 | 130 |
Q1. In which year was the gap between revenue and expenditure (the profit) the smallest, and what was it?
Q2. Revenue fell in one year compared with the year before. What was the percentage fall?
Q3. In 2024, profit was what percentage of expenditure?
| Item | Angle | Percent | Amount |
|---|---|---|---|
| Rent | 90° | 25% | ₹9,000 |
| Food | 108° | 30% | ₹10,800 |
| Education | 54° | 15% | ₹5,400 |
| Savings | 72° | 20% | ₹7,200 |
| Others | 36° | 10% | ₹3,600 |
Q1. The monthly income is ₹36,000. How much is spent on Food?
Q2. What percentage of the income goes to Savings?
Q3. Education currently takes 54°. If its spending were instead ₹12,000 out of the same income, what central angle would its sector need?
A coaching institute and its batches
A coaching institute has 800 students spread over three batches, Morning, Evening and Weekend, in the ratio 5 : 3 : 2. The girls are 40% of the Morning batch, 50% of the Evening batch and 25% of the Weekend batch. The rest of each batch are boys.
Step 1 of a caselet: turn the paragraph into a table before you read any question.
| Batch | Ratio part | Students | Girls % | Girls | Boys |
|---|---|---|---|---|---|
| Morning | 5 | 400 | 40% | 160 | 240 |
| Evening | 3 | 240 | 50% | 120 | 120 |
| Weekend | 2 | 160 | 25% | 40 | 120 |
| Total | 10 | 800 | – | 320 | 480 |
Q1. How many girls are there in the institute altogether?
Q2. What is the ratio of girls to boys in the whole institute?
Q3. The Weekend batch's boys are what percentage of all boys in the institute?
DI options are usually far apart, so exact long division is rarely needed. These tricks keep you fast without losing accuracy.
For count-type questions (how many years above a value), tick the qualifying cells while reading once. No rewriting, no calculator.
Reading tables: totals, differences, ratios →Any question about one year (best year, total of a year) lives in a single column. Add that column alone; ignore the rest of the table.
Reading tables: totals, differences, ratios →Find 1% of the base first; then any percentage is that times n. 1% of 250 is 2.5, so 70 units is 28%.
Percentage change and comparisons →A value that doubles is +100%; halves is −50%. Spot these before computing: they frame every other answer.
Percentage change and comparisons →Angle over 3.6 gives percent; angle over 36 gives percent over 10. 108° -> 30%, 54° -> 15%, 90° -> 25%.
Pie charts: degrees, shares and totals →Given one slice's value, find the value of 1 degree once, then price every other slice (and the whole pie) with one multiplication each.
Pie charts: degrees, shares and totals →Table values near a round number: average = base + (sum of differences ÷ count). 480, 520, 460, 540, 500, 500 around 500: deviations sum to 0, average exactly 500.
Averages from data →If an added value lowers the average, each old entry gains (old avg − new avg); the new entry supplies all of it.
Averages from data →Chain growth as multipliers: +10% then +10% is 1.1 x 1.1 = 1.21. One multiplication, no compounding errors.
Growth rates and successive changes →The total growth multiplier over any span is just the last value divided by the first. 144/80 = 1.8 → +80%.
Growth rates and successive changes →Turning a percentage into a fraction (or the reverse) is the quickest DI shortcut. To find 12.5% of 480, think one-eighth of 480, which is 60. To find what percentage 35 is of 280, notice 35 is one-eighth of 280, so 12.5%. Learn this short table until it is automatic. Values are rounded to two decimals where they do not terminate.
| Fraction | Percent |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.67% |
| 1/7 | 14.29% |
Also: 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%, 1/16 = 6.25%.
Examiners build wrong options out of predictable slips. Most DI errors are reading errors, not arithmetic errors.
The recurring DI question types in our notes, with how to spot each one. Open the subtopic for the formula, the steps and a worked example.
A table of items across years; the total for one item over all years is asked.
Reading tables: totals, differences, ratiosTwo entries are named (same year, different rows); their ratio is asked.
Reading tables: totals, differences, ratiosTwo rows are combined and the year with the highest combined value is asked.
Reading tables: totals, differences, ratios'For how many years was X at least / more than a value?'
Reading tables: totals, differences, ratiosThe average of one item across all columns is asked.
Reading tables: totals, differences, ratiosA table lists appeared and passed counts; the best or worst pass percentage is asked.
Reading tables: totals, differences, ratiosA table of yearly values; the percent change between two named years is asked.
Percentage change and comparisonsGrowth from the first year to the last year is asked.
Percentage change and comparisonsOne item of an expense or production table as a percent of the table's total.
Percentage change and comparisonsA table of scores or points; the question asks for the rise in points or in percent.
Percentage change and comparisonsWhich year saw the highest percentage growth?
Percentage change and comparisonsA pie of known total; one slice's angle is given and its value asked.
Pie charts: degrees, shares and totalsA share is given as a percent and the slice angle is asked (or the reverse).
Pie charts: degrees, shares and totalsTwo slices are compared as a ratio, or their value gap is asked.
Pie charts: degrees, shares and totalsThe same category appears in two pies (two years, two companies).
Pie charts: degrees, shares and totalsOne slice's value is known; the whole pie (or another slice) is asked.
Pie charts: degrees, shares and totalsA table of daily or yearly values; the overall average is asked.
Averages from dataA table pairs counts with values (staff per salary, students per mark); one average asked.
Averages from dataMachines or branches each give one output; the average output is asked.
Averages from dataAn entry is removed (lowest day) or added (seventh day) and the new average is asked.
Averages from dataA new reading must bring the average to a stated level.
Averages from dataA table of yearly values; one year's percent growth is asked.
Growth rates and successive changesThe total percentage change after two successive rises is asked.
Growth rates and successive changesThe end value and the growth rate are known; the start is asked.
Growth rates and successive changesA value table across years; which year grew at the highest rate.
Growth rates and successive changesTwo plants, shops or teams; whose growth was faster, and by how much.
Growth rates and successive changesLearn the five subtopics in order (tables, percentage, pie charts, averages, growth), then take the topic test under a timer. Afterwards, attempt a full mock and look at how long you spent on the DI block compared with the rest of the paper. Set a target per question and train to it.
Related: Data interpretation topic page · Percentage · Average · Ratio & proportion · All Quant formulas · All shortcut tricks · Formula sheet