Data Interpretation: Tables, Graphs and Data Sufficiency

Prerequisites: Data Interpretation — overview · Percentages for CSAT · Ratio, Proportion and Averages

The Hook: The Biggest Jump That Wasn’t

The Core Concept

1. The five calculations behind almost every DI question

2. Tables — worked example

Table 1. Sales of four products (thousand units). Illustrative data — not real figures.

(a) Percentage growth of P from 2021 to 2022: $\dfrac{150 - 120}{120} \times 100 = 25\%$.

(b) Which product grew most, in percentage terms, from 2021 to 2024?

R had the largest absolute rise (52 thousand) but S had the largest percentage rise.

(c) Share of R in total 2024 sales: $\dfrac{252}{615} \times 100$. Approximate: $0.4 \times 615 = 246$; the remaining 6 is about 1% of 615 → about 41%.

(d) Average annual sales of S: $\dfrac{50 + 60 + 75 + 90}{4} = \dfrac{275}{4} = 68.75$ thousand.

(e) Which products fell in some year? P in 2024 (180 → 165, −8.33%), Q in 2023 (96 → 90, −6.25%), R in 2022 (200 → 190, −5%). S never fell.

3. Bar and line graphs

• Read the axis scale and unit first — “in ₹ crore”, “in ‘000 tonnes”, “index (2015 = 100)”.
• On a line graph, the steepest segment shows the largest absolute change. It is not necessarily the largest percentage change, which depends on the starting level.
• When two series share an axis, compare their gaps for differences and their slopes for rates of change.
• Do not read values more precisely than the gridlines allow; options in CSAT are usually spaced to permit approximate reading.

4. Pie charts

A full circle is $360^\circ = 100\%$, so

Worked example. A household’s monthly income of ₹60,000 is spent as shown (illustrative data):

Trap: two pie charts for different years show shares, not amounts. A smaller slice next year can still be a larger amount if the total grew.

5. Approximation tools

• Fraction table: $\tfrac{1}{8} = 12.5\%$, $\tfrac{1}{6} = 16.67\%$, $\tfrac{1}{7} \approx 14.29\%$, $\tfrac{1}{9} \approx 11.11\%$ — see the percentages page.
• Compare fractions by cross-multiplying: is $\tfrac{46}{450}$ larger than $\tfrac{59}{496}$? $46 \times 496 = 22{,}816$ and $59 \times 450 = 26{,}550$ → the second is larger.
• Round only when options are far apart. If two options differ by less than about 2%, calculate more precisely.

6. Data sufficiency

The question asks whether the given statements are enough to answer — you need not compute the final value.

graph TD
    A[Read the question: what exactly must be fixed?] --> B{Statement 1 alone sufficient?}
    B -->|Yes| C{Statement 2 alone sufficient?}
    B -->|No| D{Statement 2 alone sufficient?}
    C -->|Yes| E[Either statement alone]
    C -->|No| F[Statement 1 alone]
    D -->|Yes| G[Statement 2 alone]
    D -->|No| H{Both together sufficient?}
    H -->|Yes| I[Both together needed]
    H -->|No| J[Neither, even together]

UPSC’s answer options for data-sufficiency questions vary in wording from question to question — read them each time and map them to the five outcomes in the diagram.

Worked example 1. What is the speed of a train?

1. It crosses a pole in 10 seconds.
2. It crosses a 200 m platform in 20 seconds.

Statement 1 alone: $L = 10v$ — two unknowns. Not sufficient. Statement 2 alone: $L + 200 = 20v$ — two unknowns. Not sufficient. Together: $10v + 200 = 20v$ → $v = 20$ m/s. Both together are needed.

Worked example 2. What is the two-digit number?

1. The sum of its digits is 9, and its tens digit is twice its units digit.
2. The number is divisible by 9.

Statement 1: $t + u = 9$ and $t = 2u$ → $u = 3$, $t = 6$ → 63. Sufficient. Statement 2: 18, 27, 36, … — many numbers. Not sufficient. Statement 1 alone.

Memory Anchors

• “Old is the base” — every percentage change divides by the earlier value.
• “3.6 degrees per per cent.”
• “Steep is big, not fast” — the steepest line segment is the largest absolute change, not necessarily the fastest growth.
• DS order: “One, Two, Then Both” — test each alone before combining; never compute more than needed.

For Prelims

Speed Strategy

• Read all the questions in a DI set before calculating. Several often need the same column totals — compute them once.
• Look at the options before calculating. If they are far apart, approximate; if close, compute precisely.
• Use the totals row. Add a “Total” row or column to the table in pencil at the start; many questions need it.
• Data sufficiency: decide sufficiency, not the value. Stop as soon as you know the answer is fixed.
• What to skip: a DI set with many columns and a dense, unfamiliar layout can consume ten minutes. Attempt one question; if it takes over two minutes, move on and return later.

Common Traps

Practice

Prelims (CSAT)

Questions 1–3 are based on Table 1 above (illustrative data).

Quick Revision

Key Takeaways

Related Topics

• Data Interpretation — quick revision
• Data Interpretation — practice questions
• Percentages for CSAT
• Ratio, Proportion and Averages for CSAT
• Time, Speed, Distance and Work