Data Interpretation

Tables, bar charts, pie charts, line graphs

127 practice questionsPage updated 5 Apr 2026Review metadata pendingPractice questions

Data Interpretation (DI) is the process of making sense of numerical data that has been collected, analysed and presented. In aptitude exams, DI questions typically present data in the form of tables, bar charts, pie charts, line graphs, or caselets, and test your ability to extract relevant information, perform calculations, and draw logical conclusions.

Key formulas and rules

Percentage = (Part/Whole) x 100

Percentage Change = [(New Value - Old Value)/Old Value] x 100

Percentage Point Change = New Percentage - Old Percentage

Ratio = Value A : Value B = (Value A)/(Value B)

Average = Sum of all values / Number of values

If A is X% more than B, then B is [X/(100+X)] x 100% less than A

If A is X% less than B, then B is [X/(100-X)] x 100% more than A

Successive Percentage Change: a% followed by b% = (a + b + ab/100)%

Compound Growth Rate: Final = Initial x (1 + r/100)^n

Key concepts

Types of Data Presentation

Tables: Data arranged in rows and columns, best for exact values and comparisons. Bar Charts: Vertical or horizontal bars representing quantities, good for comparing discrete categories. Pie Charts: Circular representation showing parts of a whole as sectors, ideal for percentage distributions. Line Graphs: Points connected by lines showing trends over time, perfect for time-series analysis. Caselets: Paragraph-based data requiring extraction and organisation before solving.

Percentage Calculations in DI

Most DI questions revolve around percentages. Key operations include: finding what percentage one value is of another, calculating percentage increase/decrease, determining percentage point differences, and computing successive percentage changes. Always identify the base (reference) value correctly — a common error is using the wrong denominator. For pie charts, remember all sectors sum to 100% or 360 deg.

Worked examples

Example 1

Study the following table and answer: In which year was the percentage increase in exports maximum?

Year | 2020 | 2021 | 2022 | 2023 | 2024
Exports | 200 | 250 | 300 | 360 | 450 (in Rs. crores)

Solution

Step 1: Calculate absolute and percentage increase for each year.
Step 2: 2020->2021: Increase = 250-200 = 50. % increase = (50/200)x100 = 25%
Step 3: 2021->2022: Increase = 300-250 = 50. % increase = (50/250)x100 = 20%
Step 4: 2022->2023: Increase = 360-300 = 60. % increase = (60/300)x100 = 20%
Step 5: 2023->2024: Increase = 450-360 = 90. % increase = (90/360)x100 = 25%
Step 6: Both 2021 and 2024 show 25% increase. However, the question asks for the year IN WHICH the increase was maximum — referring to the target year.
Answer: 2024 (highest absolute increase of 90 crores, equal highest percentage at 25%, and most recent).

Example 2

In a pie chart showing monthly expenses: Rent = 30%, Food = 25%, Transport = 15%, Entertainment = 20%, Savings = 10%. If total monthly income is Rs. 50,000, by what percentage should transport expenses be reduced so that savings become 20% of income?

Solution

Step 1: Current savings = 10% of 50,000 = Rs. 5,000.
Step 2: Target savings = 20% of 50,000 = Rs. 10,000.
Step 3: Required increase in savings = 10,000 - 5,000 = Rs. 5,000.
Step 4: This must come from reduced transport expenses.
Step 5: Current transport = 15% of 50,000 = Rs. 7,500.
Step 6: New transport = 7,500 - 5,000 = Rs. 2,500.
Step 7: Reduction in transport = 5,000.
Step 8: Percentage reduction = (5,000/7,500)x100 = 66.67% or 66 %
Answer: 66.67% (or 200/3%)

Example 3

A line graph shows company profits (in lakhs): 2019: 120, 2020: 150, 2021: 180, 2022: 135, 2023: 195. What is the average annual growth rate from 2019 to 2023?

Solution

Step 1: Initial value (2019) = 120 lakhs
Step 2: Final value (2023) = 195 lakhs
Step 3: Time period = 4 years
Step 4: Using CAGR formula: [(Final/Initial)^(1/n) - 1] x 100
Step 5: (195/120) = 1.625
Step 6: (1.625)^(1/4) = (1.625)^0.25 ~= 1.129
Step 7: Growth rate = (1.129 - 1) x 100 = 12.9%
Step 8: Alternative simple average: Total growth = (195-120)/120 x 100 = 62.5%. Average = 62.5/4 = 15.625%
Answer: Approximately 12.9% CAGR (or 15.6% simple average depending on method specified).

Example 4

In a bar chart of student enrollment across 5 colleges (A: 1200, B: 1500, C: 1800, D: 900, E: 1600), if 60% students in College C are boys and 55% students in College E are girls, what is the ratio of girls in C to boys in E?

Solution

Step 1: Students in College C = 1800
Step 2: Boys in C = 60% of 1800 = 0.60 x 1800 = 1080
Step 3: Girls in C = 1800 - 1080 = 720
Step 4: Students in College E = 1600
Step 5: Girls in E = 55% of 1600 = 0.55 x 1600 = 880
Step 6: Boys in E = 1600 - 880 = 720
Step 7: Ratio of girls in C to boys in E = 720 : 720 = 1 : 1
Answer: 1:1

Student	Maths	Science	English
A	85	78	92
B	72	88	85
C	90	82	78

Data Interpretation

Key formulas and rules

Key concepts

Types of Data Presentation

Percentage Calculations in DI

Ratio and Proportion

Growth and Trends Analysis

Approximation Techniques

Data Sufficiency in DI

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Types of Data Presentation

Percentage Calculations in DI

Ratio and Proportion

Growth and Trends Analysis

Approximation Techniques

Data Sufficiency in DI

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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