Chapter 7 · Topic 7.1 · Prelims + Mains1 of 3
Data Interpretation & Data Sufficiency (Class X level): Tables and graphs
Key points
- DI gives a table or graph and asks for a value, ratio or trend; DS asks only whether the statements are enough.
- Trend: 2011 to 2015 had 25 DI and 0 DS; 2021 to 2026 had 4 DI and 28 DS.
- Percentage change = (new − old) ÷ old × 100; pie share = angle ÷ 360°.
- Trap: a falling growth rate does not mean a falling total.
Prelims box: facts and traps
- DS answers: (a) one alone works; (b) either alone works; (c) only both together; (d) not even both.
- Census: growth 2001 to 2011 ≈ 17.7%; 1991 to 2001 ≈ 21.5%.
How CSAT asks data questions
Like a shopkeeper’s bill: DI asks “what is the total?”; DS asks “do I have enough information to work out the total?”
| CSAT years | Data interpretation | Data sufficiency |
|---|---|---|
| 2011 to 2015 | 25 | 0 |
| 2016 to 2020 | 16 | 5 |
| 2021 to 2026 | 4 | 28 |
Battle IAS classification of the 78 questions tagged data interpretation or sufficiency in the CSAT PYQ book, topic 8: items with two statements and no graph or table counted as DS. Approximate; 2026 answers provisional.
The trend is clear: graph-heavy DI sets were common up to 2018; since 2022 the block is mostly data sufficiency. Both need the same arithmetic as Basic Numeracy.
The four DS answers:
- (a) one statement alone works but the other does not.
- (b) either statement alone works.
- (c) only both together work.
- (d) even both together do not work.
Data sufficiency in four steps (Battle IAS method): always test I alone, then II alone, then both, then pick the matching option.
What UPSC asks: Prelims: DI vs DS; DS rose after 2021. Next likely angle: the four DS answers.
Data interpretation: tables, bars, lines and pies
Read the title, the units and the scale before the numbers. Most DI questions need one of four things:
- a difference;
- a ratio;
- a percentage change: (new − old) ÷ old × 100;
- a pie share: angle ÷ 360°.
Round sensibly when the options are far apart.
| Census year | Population of India (crore) | Type |
|---|---|---|
| 1981 | 68.33 | Census of India (measured; includes an interpolated figure for Assam, where the census was not held) |
| 1991 | 84.64 | Census of India (measured; includes a projected figure for Jammu and Kashmir, where the census was not held) |
| 2001 | 102.87 | Census of India (measured) |
| 2011 | 121.09 | Census of India (measured) |
Source: Census of India, Office of the Registrar General and Census Commissioner, final population totals.
Worked practice on the table (Battle IAS calculation):
- Growth 2001 to 2011 = (121.09 − 102.87) ÷ 102.87 × 100 = 18.22 ÷ 102.87 × 100 ≈ 17.7%.
- Growth 1991 to 2001 = 18.23 ÷ 84.64 × 100 ≈ 21.5%.
- The population added was almost the same (about 18.2 crore) in both decades, but the growth rate fell because the base was larger.
Pie charts: a share of 25% is 90°; 10% is 36°. If items take 90°, 50°, 45° and 75°, the rest is 360 − 260 = 100°.
Line graphs: a steeper line means a faster change; a falling growth rate can still mean a rising total.
Common trap: “the growth rate fell” does not mean “the population fell”. Read whether the graph shows a level or a rate.
What UPSC asks: Prelims: read units first; % change = change ÷ old. Next likely angle: level vs rate.
Practice
Practice MCQs (8)
The table below gives the rice production (in lakh tonnes) of four States P, Q, R and S from 2021 to 2024. Year | P | Q | R | S 2021 | 40 | 35 | 25 | 20 2022 | 44 | 33 | 30 | 21 2023 | 48 | 36 | 27 | 24 2024 | 50 | 42 | 33 | 25 By what percentage did the rice production of State P increase from 2021 to 2024?
Answer (a) & explanation
Step 1: P produced 40 lakh tonnes in 2021 and 50 lakh tonnes in 2024. Step 2: Increase = 50 − 40 = 10 lakh tonnes. Step 3: Percentage increase = increase ÷ starting value × 100 = 10 ÷ 40 × 100 = 25%.
A bar chart shows the number of students (in thousands) enrolled in five streams of a State's colleges in 2024 and 2025. The bar heights are as follows. Stream | 2024 | 2025 Arts | 50 | 45 Science | 40 | 47 Commerce | 30 | 36 Engineering | 35 | 31 Medicine | 15 | 17 By how many students did the total enrolment in the five streams increase from 2024 to 2025?
Answer (d) & explanation
Step 1: Total for 2024 = 50 + 40 + 30 + 35 + 15 = 170 thousand. Step 2: Total for 2025 = 45 + 47 + 36 + 31 + 17 = 176 thousand. Step 3: Increase = 176 − 170 = 6 thousand = 6,000 students.
A line graph shows the revenue and the expenditure (in ₹ crore) of a company from 2020 to
2024. The plotted values are as follows. (Profit = Revenue − Expenditure.) Year | Revenue | Expenditure 2020 | 120 | 100 2021 | 130 | 115 2022 | 150 | 120 2023 | 140 | 125 2024 | 180 | 145 Consider the following statements based on the line graph:
1. The company's revenue increased every year from 2020 to 2024.
2. The company's expenditure increased every year from 2020 to 2024.
3. The company's average annual profit over the five years was ₹23 crore.
Which of the statements given above is/are correct?
Answer (c) & explanation
Step 1 (Statement 1): Revenue went 120, 130, 150, then fell to 140 in 2023, then 180: incorrect. Step 2 (Statement 2): Expenditure 100, 115, 120, 125, 145 rises every year: correct. Step 3 (Statement 3): Profits 20 + 15 + 30 + 15 + 35 = 115; 115 ÷ 5 = 23: correct.
A line graph shows the revenue and the expenditure (in ₹ crore) of a company from 2020 to
2024. The plotted values are as follows. (Profit = Revenue − Expenditure.) Year | Revenue | Expenditure 2020 | 120 | 100 2021 | 130 | 115 2022 | 150 | 120 2023 | 140 | 125 2024 | 180 | 145 In which year was the company's profit, expressed as a percentage of its expenditure, the highest?
Answer (b) & explanation
Step 1: Profit = Revenue − Expenditure: 2020: 20; 2021: 15; 2022: 30; 2023: 15; 2024: 35. Step 2: Profit % = profit ÷ expenditure × 100: 2020: 20%; 2021: about 13%; 2022: 30/120 = 25%; 2023: 12%; 2024: 35/145 ≈ 24.1%. Step 3: The highest is 2022, although the largest profit in crore is in 2024.
The table below gives the rice production (in lakh tonnes) of four States P, Q, R and S from 2021 to 2024. Year | P | Q | R | S 2021 | 40 | 35 | 25 | 20 2022 | 44 | 33 | 30 | 21 2023 | 48 | 36 | 27 | 24 2024 | 50 | 42 | 33 | 25 In which year was the share of State R in the total rice production of the four States the highest?
Answer (b) & explanation
Step 1: Find each year's total: 2021: 120; 2022: 128; 2023: 135; 2024: 150. Step 2: R's share = R ÷ total. 2021: 25/120 ≈ 20.8%; 2022: 30/128 ≈ 23.4%; 2023: 27/135 = 20%; 2024: 33/150 = 22%. Step 3: The highest share is in 2022, even though R's largest output was in 2024.
A pie chart shows how a family's total monthly income of ₹48,000 is distributed. The share of each head, as a percentage of the total, is given below. Head | Share (%) Food | 30 Rent | 25 Education | 15 Transport | 10 Savings | 12 Others | 8 By how many rupees does the family's monthly expenditure on Rent exceed its expenditure on Transport?
Answer (d) & explanation
Step 1: Rent is 25% and Transport is 10%, so the difference is 15 percentage points. Step 2: 15% of ₹48,000 = 0.15 × 48,000 = ₹7,200. (Check: Rent = ₹12,000 and Transport = ₹4,800; 12,000 − 4,800 = 7,200.)
The table below gives the rice production (in lakh tonnes) of four States P, Q, R and S from 2021 to 2024. Year | P | Q | R | S 2021 | 40 | 35 | 25 | 20 2022 | 44 | 33 | 30 | 21 2023 | 48 | 36 | 27 | 24 2024 | 50 | 42 | 33 | 25 Consider the following statements based on the table:
1. State Q's production fell, compared with the previous year, in exactly one year.
2. The average annual production of State S over the four years is 22.5 lakh tonnes.
3. In every year, State P produced more rice than States R and S together.
4. The total production of the four States rose every year.
How many of the statements given above are correct?
Answer (c) & explanation
Step 1 (Statement 1): Q: 35 → 33 (fall in 2022) → 36 → 42. Exactly one fall: correct. Step 2 (Statement 2): S: 20 + 21 + 24 + 25 = 90; 90 ÷ 4 = 22.5: correct. Step 3 (Statement 3): In 2021, R + S = 25 + 20 = 45, more than P's 40: incorrect. Step 4 (Statement 4): Totals 120, 128, 135, 150 rise every year: correct. Three statements are correct.
A bar chart shows the number of students (in thousands) enrolled in five streams of a State's colleges in 2024 and 2025. The bar heights are as follows. Stream | 2024 | 2025 Arts | 50 | 45 Science | 40 | 47 Commerce | 30 | 36 Engineering | 35 | 31 Medicine | 15 | 17 In 2025, by approximately what percentage was the enrolment in Science more than the enrolment in Engineering?
Answer (a) & explanation
Step 1: In 2025, Science = 47 thousand and Engineering = 31 thousand. Step 2: Difference = 16 thousand. Step 3: 'More than Engineering' makes Engineering the base: 16 ÷ 31 × 100 ≈ 51.6%.
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In 150 words, explain the significance of Data Interpretation & Data Sufficiency with one recent example.
Flashcards (9)
DS answer (a) means?
One statement alone works, the other does not.
DS answer (b)?
Either statement alone works.
DS answer (c)?
Only both together work.
DS answer (d)?
Even both together do not work.
Which block grew in CSAT after 2021?
Data sufficiency.
Percentage change formula?
(new − old) ÷ old × 100.
25% of a pie in degrees?
90°.
India's decadal population growth 2001 to
2011 (Census)? About 17.7%.
Falling growth rate means falling
population? No, the total can still rise.
Next topic · 7.2 →Data Interpretation & Data Sufficiency (Class X level): Data sufficiency with numbers