Data Interpretation

Snapshot

• Data Interpretation (DI) gives you information as a chart, graph or table and asks 3–5 questions that you answer by calculating, not by recalling facts. In the CUET General Test it is one of the highest-return topics: the data is on the screen, so a trained student converts it almost directly into marks.
• Questions arrive as a set of 4–5 built on one chart, so the 20–30 seconds you spend understanding the chart pays off across several marks.
• This guide teaches the whole topic from the ground up — the five data formats (with worked diagrams), the core toolkit of percentage, ratio, average and change, a repeatable solving method, and a deep speed-techniques section.
• Exam reality: +5 correct, −1 wrong. Accuracy first, then speed.

Part 1 — Read the chart before you calculate

Most lost DI marks come not from weak arithmetic but from misreading the chart. Learn what each format shows.

Tables

Rows and columns of exact numbers — the most information-dense format. The single most important thing is the unit in the heading ("₹ in lakh", "in thousands", "% of total"). Find the unit and the exact row/column you need before touching a question.

Bar charts

Bars whose height equals a value. Tell the three sub-types apart: simple (one bar per category), grouped (two or more bars per category — read the legend), and stacked (segments of one bar that add up to a total). The dashed line below marks the average — a very common add-on question.

Line graphs

Points joined over time. Line graphs are about trend and rate of change, so "between which two years did sales rise the most?" is asking for the steepest segment — which is often not the highest point. Train your eye to read slopes, not heights.

Pie charts

A circle split into slices that share one whole. A slice is given as a percentage or in degrees; convert with 1% = 3.6° (since 100% = 360°). If a total value is given, a slice's value = slice% × total.

Caselets

A short paragraph that hides the data in sentences, with no chart drawn. The skill is organising data: underline every number and label, and draw your own tiny table. A caselet then becomes an ordinary table question.

Part 2 — The core toolkit (the only math you need)

Percentage

"What percent is A of B" = (A ÷ B) × 100. Memorise these fraction–percent pairs so you never long-divide:

Two time-savers: flip it ("16% of 25" = "25% of 16" = 4), and reverse percentage (if 120 is 80% of a number, the number is 120 ÷ 0.8 = 150).

Ratio

A ratio A : B compares two quantities, reduced to lowest terms. Three variations: combined "(A + C) : (B + D)" — add first, then reduce; share of total = A ÷ (A + B + C); and dividing a quantity — to split ₹1,800 in 2 : 3 : 4, one unit = 1800 ÷ 9 = ₹200, giving ₹400, ₹600, ₹800.

Average

Average = (sum of values) ÷ (number of values). For a missing value: missing = average × count − (sum of the known values). For unequal groups use the weighted average: (n₁·a₁ + n₂·a₂) ÷ (n₁ + n₂) — a class of 40 averaging 60 and a class of 60 averaging 70 combine to (2400 + 4200) ÷ 100 = 66, not 65.

Percentage change — the most-tested, most-failed idea

% change = (new − old) ÷ OLD × 100. Divide by the old value, every time. Rise from 50 to 60 = 10 ÷ 50 = 20% (not 16.67%). Three deeper points: successive change (10% up then 10% down = net 1% down; for two changes net % = a + b + ab ÷ 100); percentage point vs percent (20% → 25% is 5 points but a 25% relative rise); and growth vs gap (a ₹10 cr rise on ₹40 cr beats the same rise on ₹50 cr).

Part 3 — A repeatable method for any DI set

1. Read the title and units first — half of all DI traps live in the units.
2. Scan the legend and axes before reading a single question.
3. Extract only what the question asks — never compute the whole table.
4. Estimate, then refine — if options are far apart, a rounded estimate already wins.

Part 4 — Speed techniques (where the marks are won)

Everyone can eventually get a DI answer; the exam rewards getting it in under a minute.

1. Estimate aggressively when options are spread out. "Approximately" is permission to round: 197 ÷ 4.1 ≈ 200 ÷ 4 = 50.
2. Convert every percentage to a fraction. 37.5% of 800 = 3/8 × 800 = 300 in one step.
3. Use complementary percentages. If 78% is spent, 22% is saved — compute the friendlier one.
4. Eliminate by magnitude. A percentage can't exceed 100; a part can't exceed its whole — cross out impossible options on sight.
5. Reuse the denominator. The total you found for Q1 is usually the base for Q2–Q4; write it once.
6. Read the chart once, up front. Invest 20–30 seconds before Q1 instead of re-reading for each question.
7. Round to anchor numbers (10, 25, 50, 100): 48.7% of 1,024 ≈ half of 1,000 ≈ 500.
8. Use unit-value for ratios — find one unit first, then every part is one multiplication.
9. Sanity-check the size. An increase must be bigger than the original; a discount must be smaller — this catches base-value slips instantly.

Part 5 — Worked examples (with the chart in front of you)

Example 1 — bar chart, average & counting. In how many of the five years was the figure below the five-year average?

Average = (30 + 45 + 25 + 50 + 40) ÷ 5 = 190 ÷ 5 = 38 (the dashed line). Values below 38: 30 (2018) and 25 (2020) → 2 years.

Example 2 — pie chart, percent & degrees.

How much more is spent on Rent than Travel? (30% − 15%) × 40,000 = ₹6,000. Savings slice in degrees? 20% × 360° = 72°.

Example 3 — line graph, highest growth (gap vs growth trap). Which year had the highest percentage growth over the previous year?

2020 = 10/40 = 25%; 2021 = 10/50 = 20%; 2022 = 30/60 = 50% → 2022. Note 2020 and 2021 had the same ₹10 cr rise but different percentages — never judge growth by the gap alone.

Example 4 — caselet, multi-step. "A school has 600 students; 60% are boys. 25% of the boys and 50% of the girls play a sport." Boys = 360, Girls = 240. Sport = 25% of 360 + 50% of 240 = 90 + 120 = 210.

Part 6 — Common mistakes & NTA traps

• Base trap — percentage change is on the old value, always.
• Unit trap — mixing "in thousands" with absolute numbers, or pie percent with degrees (1% = 3.6°).
• Gap vs growth — the biggest rise in value is not always the biggest percentage rise.
• Percentage point vs percent — read which one is asked.
• Off-by-one counting — "at least", "more than", "below" each shift the count by one.
• Average ≠ middle bar — always compute it.

Part 7 — How to use this page

1. Read Parts 1–2 until the formats and four calculations feel automatic.
2. Re-solve the four worked examples with the page scrolled away, writing each step.
3. Attempt the practice questions below; for any you miss, name the tool (Part 2) or trap (Part 6) that caught you.
4. Finish with the timed practice test to build exam-day speed using Part 4.

One-line revision: read the units first, convert percentages to fractions, divide percentage change by the old value, compare percentages (not gaps) for "highest growth", weight your averages when groups differ, and estimate whenever the options are spread out.