Data Interpretation

Snapshot

• Data Interpretation (DI) gives you numbers as a table, bar chart, line graph, pie chart or short paragraph, then asks 3 to 5 questions that you answer by calculating, not by recalling facts. The data is on the screen, so a trained student turns it almost directly into marks.
• CUET asks the same handful of calculations again and again: percentage of a total, percentage change, ratio, average, difference, and "which year or item is highest".
• The idea that cracks it: read the title, units and legend before any question, then use the quickest tool: fraction instead of percentage, estimate when the options are far apart.
• Marking is +5 / −1. Accuracy first, then speed: a set shares one chart, so 30 seconds spent reading it pays across every question.

Part 1 — Read the chart before you calculate

Written and reviewed by Devendra Dubey, Mathematics & Commerce faculty at UniDrill (M.Sc. Mathematics, Osmania University · 10 years teaching). Prepared for the CUET UG General Test.

Most lost DI marks come from misreading the chart, not from weak arithmetic. Learn what each format shows and what it hides.

Tables

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

Bar charts

Bars whose height equals a value. Tell the three kinds apart: simple (one bar per category), grouped (two or more bars per category, so read the legend), and stacked (segments of one bar that add up to a total).

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?" asks for the steepest segment, which is often not the highest point.

Pie charts

A circle split into slices that share one whole. A slice is given as a percentage or in degrees, and you convert with $1\% = 3.6^\circ$ (since $100\% = 360^\circ$). If a total value is given, a slice's value is the slice percentage times the total.

Caselets

A short paragraph that hides the data in sentences, with no chart drawn. The skill is organising the 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 maths you need)

Percentage

$\text{A as a percentage of B} = \dfrac{A}{B} \times 100$. Memorise these fraction and percentage pairs so you never long-divide:

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

Percentage change

$$\%\ \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$$

Divide by the old value every time. A rise from 50 to 60 is $\dfrac{10}{50} = 20\%$, not 16.67%. For two changes in a row of $a\%$ and $b\%$, the net change is $a + b + \dfrac{ab}{100}$ percent, so 10% up then 10% down is $10 - 10 - 1 = -1\%$, a net fall of 1%.

Percentage points versus percent

If a pass rate goes from 20% to 25%, it rose by 5 percentage points, but the relative rise is $\dfrac{5}{20} = 25\%$. Read which one the question asks for.

Ratio

A ratio $A : B$ compares two quantities, reduced to lowest terms. For a combined ratio, add first and then reduce. For a share of a total, use $\dfrac{A}{A+B+C}$. To split a quantity in a ratio, find one unit first: to split ₹1,800 in the ratio $2:3:4$, one unit is $1800 \div 9 = 200$, giving ₹400, ₹600 and ₹800.

Average

$$\text{average} = \frac{\text{sum of values}}{\text{number of values}}$$

For a missing value: missing $=$ average $\times$ count $-$ sum of the known values. For unequal groups use the weighted average $\dfrac{n_1 a_1 + n_2 a_2}{n_1 + n_2}$: a class of 40 averaging 60 and a class of 60 averaging 70 combine to $\dfrac{2400 + 4200}{100} = 66$, not 65.

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, axes and footnotes before you read any question.
3. Write down what the question asks, and extract only those numbers. Never compute the whole table.
4. Choose the tool: percentage of total, percentage change, ratio, average or difference.
5. Estimate first. If the options are far apart, a rounded estimate already wins.
6. Calculate with fractions, not decimals, wherever you can.
7. Check the size of your answer: an increase must exceed the original, a percentage cannot pass 100% unless it is an increase, and a part cannot exceed its whole.

Part 4 — The full menu of question types

Part 5 — 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 when options are spread out. "Approximately" is permission to round: $197 \div 4.1 \approx 200 \div 4 = 50$.
2. Turn percentages into fractions. 37.5% of 800 is $\tfrac{3}{8} \times 800 = 300$.
3. Use complements. If 78% is spent, 22% is saved, and 22% is usually the friendlier number.
4. Eliminate by magnitude. Cross out impossible options at once: a part larger than its whole, a share above 100%.
5. Reuse the denominator. The total you found for the first question is the base for the next two.
6. Round to anchors (10, 25, 50, 100): 48.7% of 1,024 is close to half of 1,000, so about 500.
7. Find the unit first in ratio questions, then each part is one multiplication.
8. Compare fractions by cross-multiplying when two percentages are close: $\tfrac{7}{19}$ against $\tfrac{3}{8}$ becomes $7 \times 8 = 56$ against $3 \times 19 = 57$.
9. Sanity-check the answer's size before moving on. It catches base-value slips instantly.

Part 6 — Worked examples

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

Average $= \dfrac{30 + 45 + 25 + 50 + 40}{5} = \dfrac{190}{5} = 38$, shown as the dashed line. The years below 38 are 2018 (30) and 2020 (25), so the answer is 2 years.

Example 2. Pie chart, difference and degrees. How much more is spent on Rent than on Travel, and what is the central angle of the Savings slice?

Rent minus Travel is $(30\% - 15\%) \times 40{,}000 =$ ₹6,000. Savings is $20\% \times 360^\circ =$ 72°.

Example 3. Line graph, highest growth. Which year had the highest percentage growth over the previous year?

2020: $\dfrac{10}{40} = 25\%$. 2021: $\dfrac{10}{50} = 20\%$. 2022: $\dfrac{30}{60} = 50\%$. The answer is 2022. Notice that 2020 and 2021 had the same ₹10 crore rise but different percentages, so never judge growth by the gap alone.

Example 4. A table with several questions. Sales of four products (₹ lakh):

(a) What percentage of the 2024 total is Q? (b) What is the percentage growth of the total from 2023 to 2024? (c) Which product grew fastest from 2022 to 2024? (d) Which product fell from 2023 to 2024, and by what percentage?

(a) $\dfrac{45}{150} = 30\%$. (b) $\dfrac{150 - 120}{120} = \dfrac{30}{120} =$ 25%. (c) P: $\dfrac{20}{40} = 50\%$, Q: $\dfrac{15}{30} = 50\%$, R: $\dfrac{4}{20} = 20\%$, S: $\dfrac{11}{10} = 110\%$, so S grew fastest. (d) Only R fell, by $\dfrac{6}{30} =$ 20%.

Example 5. Pie chart with a total. A company's expenditure of ₹12,00,000 is split as below.

(a) How much is spent on raw material? (b) How much more is spent on salaries than rent? (c) What is the central angle for Marketing? (d) If Marketing spending rises by 25% and everything else stays the same, what share of the new total is Marketing?

(a) $25\% \times 12{,}00{,}000 =$ ₹3,00,000. (b) $(35\% - 20\%) = 15\%$ of ₹12,00,000 $=$ ₹1,80,000. (c) $12 \times 3.6^\circ =$ 43.2°. (d) Marketing is ₹1,44,000, and a 25% rise makes it ₹1,80,000. The total becomes $12{,}00{,}000 + 36{,}000 = 12{,}36{,}000$, so the share is $\dfrac{1{,}80{,}000}{12{,}36{,}000} \approx$ 14.56%, not 15%, because the total also grew.

Example 6. A line graph with two lines. The graph shows exports and imports (₹ crore).

(a) In which year was the surplus (exports minus imports) the largest? (b) By what percentage did exports rise from 2020 to 2023? (c) What is the net balance over the four years?

Surplus by year: $60 - 50 = +10$, $70 - 75 = -5$, $95 - 80 = +15$, $100 - 120 = -20$. (a) The largest surplus is in 2022. (b) $\dfrac{100 - 60}{60} = \dfrac{2}{3} \approx$ 66.7%. (c) $10 - 5 + 15 - 20 =$ 0, because both lines total 325.

Example 7. A pie chart with a table. A college has 600 students: Science 40%, Commerce 35%, Arts 25%. The percentage of girls in each stream is Science 30%, Commerce 40%, Arts 60%. (a) What percentage of all students are girls? (b) What is the ratio of boys to girls? (c) What percentage of all girls are in Arts?

Students: Science 240, Commerce 210, Arts 150. Girls: $0.30 \times 240 = 72$, $0.40 \times 210 = 84$, $0.60 \times 150 = 90$, total 246. (a) $\dfrac{246}{600} =$ 41%. (b) Boys are $600 - 246 = 354$, so boys : girls $= 354 : 246 =$ 59 : 41. (c) $\dfrac{90}{246} = \dfrac{15}{41} \approx$ 36.6%.

Example 8. A grouped bar read as numbers. Enrolment in a coaching centre:

(a) In which year was the girls' share the highest? (b) By what percentage did the total enrolment in 2023 exceed that in 2021?

(a) Shares: 2021, $\dfrac{80}{200} = 40\%$. 2022, $\dfrac{100}{250} = 40\%$. 2023, $\dfrac{160}{300} \approx 53.3\%$. The answer is 2023. (b) Totals are 200 and 300, so $\dfrac{300 - 200}{200} =$ 50%.

Example 9. Percentage points versus percent. A school's pass rate rose from 60% to 75%. State the rise in percentage points and the relative rise.

The rise is $75 - 60 =$ 15 percentage points. The relative rise is $\dfrac{15}{60} =$ 25%.

Example 10. Missing value from an average. The average sales of four quarters is 45 (in thousands). The first three quarters are 40, 50 and 35. Find the fourth.

Total $= 45 \times 4 = 180$. The first three add to 125. The fourth quarter is $180 - 125 =$ 55 thousand.

Example 11. Successive change. A town's population grows by 20% in 2022 and falls by 10% in 2023. If it was 50,000 at the start, what is it after two years, and what is the net change?

Net change $= 20 - 10 + \dfrac{20 \times (-10)}{100} = 8\%$. Population $= 50{,}000 \times 1.08 =$ 54,000, which is also $50{,}000 \times 1.2 \times 0.9$.

Example 12. A caselet with nested percentages. A village has 5,000 people. 60% are literate. Among the literate, 55% are male. Among the illiterate, 45% are male. What percentage of the village is male?

Literate $= 3{,}000$, so literate males $= 0.55 \times 3000 = 1{,}650$. Illiterate $= 2{,}000$, so illiterate males $= 0.45 \times 2000 = 900$. Total males $= 2{,}550$, which is $\dfrac{2550}{5000} =$ 51%.

Example 13. A caselet with a ratio. In a class the ratio of boys to girls is 3 : 2. 40% of boys and 50% of girls wear glasses. What percentage of the class wears glasses?

Take 50 students so the ratio is easy: 30 boys and 20 girls. Glasses: $0.40 \times 30 = 12$ and $0.50 \times 20 = 10$, a total of 22. $\dfrac{22}{50} =$ 44%. Any class size in the ratio $3 : 2$ gives the same percentage.

Part 7 — Common mistakes and traps

Part 8 — Rapid-fire practice with answers

Part 9 — A timed-practice routine

In the exam, read the chart once, then do the read-off and estimate questions first. Leave a multi-step caselet question until the other questions in the set are done, because the totals you find for the easy questions often help. After every practice set, name the tool or the trap that caused each wrong answer.

Part 10 — Where this connects

DI draws on Arithmetic for percentages and ratios, on Averages & Ages for the weighted average and missing-value tricks, and on Profit, Loss & Interest for the successive-change and base-value ideas. Pie angles and areas link with Mensuration & Basic Geometry, and spotting the pattern across a row of numbers is the same habit as in Series.

One-line revision: read the units first, convert percentages to fractions, divide percentage change by the old value, compare percentages rather than gaps for "highest growth", weight your averages when groups differ, and estimate whenever the options are spread out.