14  Data Interpretation

14.1 Introduction

Data Interpretation (DI) is the application of basic arithmetic and logical reasoning to interpret tabular, graphical, and chart-based data.
It tests your ability to quickly process numbers, compare values, compute percentages/ratios, and infer insights.
This is a high-scoring but time-sensitive section in exams like IPMAT.

Common DI formats include:
- Tables (row/column data)
- Bar graphs and column graphs
- Line graphs (trend over time)
- Pie charts
- Caselets (paragraph data)
- Mixed graphs

14.2 1) Core DI Skills

  • Percentages and Ratios: Most DI questions reduce to these.
  • Averages and Weighted Averages: Compute across groups.
  • Difference/Gap analysis: Increase/decrease, male vs female, product A vs product B.
  • Approximation: Use rounding to save time when options are far apart.

14.3 2) Table-Based DI

14.3.1 Example

The table shows sales (in lakh rupees) of 4 companies over 3 years:

Company 2021 2022 2023
A 120 150 180
B 100 130 160
C 140 160 190
D 90 120 150

Q1. Which company had highest growth rate 2021→2023?
- Compute percentage growth: e.g., A = (180−120)/120×100=50%.
- Similarly for others; answer = Company B (60%).

14.4 3) Bar Graphs

Bar graphs compare discrete categories.

14.4.1 Example

Marks scored by 5 students:

Student Marks
P 60
Q 75
R 50
S 80
T 70

Q. Average marks?
= (60+75+50+80+70)/5 = 67.

14.5 4) Line Graphs

Line graphs show trends across time.

14.5.1 Example

Monthly revenue of a shop (in ₹000):

Month Jan Feb Mar Apr May
Rev 20 25 30 22 28

Q. What is percentage drop from Mar to Apr?
= (30−22)/30 ×100 = 26.67%.

14.6 5) Pie Charts

Pie charts represent data as percentage shares of a whole (360°).

14.6.1 Example

Company expenses: Rent 25%, Salaries 35%, Materials 20%, Marketing 15%, Misc 5%.
If total = ₹20 lakh, marketing = 15% of 20 lakh = ₹3 lakh.

14.7 6) Caselets

A caselet provides data in a paragraph instead of a table/graph.

Example:
A class of 120 students: 45% girls, 30% of boys play cricket, 40% of girls play cricket.
Find number of students playing cricket.

  • Girls = 54, Boys = 66.
  • Girls playing cricket = 54×0.4=22.
  • Boys playing cricket = 66×0.3=20.
  • Total = 42.

14.8 7) Mixed Graphs

Exams may combine bar + line, or table + pie.
Strategy:
- Identify base of percentages.
- Translate visual data into actual numbers.
- Beware of scaling (axes, pie %).

14.9 8) Common Traps

  • Using wrong base in percentages.
  • Confusing absolute increase with percentage increase.
  • Ignoring units (lakh, crore, %, ratio).
  • Over-calculating when approximation is enough.

14.10 9) Solved Practice Questions

Ex 1. In a pie chart, sector = 90°. What % of total?
= 90/360×100 = 25%.

Ex 2. In a table, production increases from 200 to 260. % increase?
= 60/200×100 = 30%.

Ex 3. If average of 4 items is 50 and total of 3 items is 130, find 4th.
= 200−130 = 70.

Ex 4. From a bar graph: Sales = 150, Cost = 120. Find profit%.
= (30/120)×100 = 25%.

Ex 5. In a caselet: 500 employees, 40% women, 20% men in HR, 30% women in HR. Find HR staff.
Men = 300, women = 200. HR men=60, HR women=60. Total HR=120.

14.11 10) Practice Set

14.11.1 Set A – Fundamentals

  1. A bar graph shows monthly sales: Jan=200, Feb=240, Mar=300, Apr=260. Find average sales.
  2. A pie chart shows market share: A=40%, B=35%, C=25%. If total market = 200 crore, find C’s sales.
  3. A line graph shows production: 2021=400, 2022=480, 2023=600. Find % growth 2021→2023.
  4. A table shows profit% of 4 shops: 10%, 20%, 15%, 25%. If CP for each = 200, find average SP.
  5. A caselet: In a college of 1000 students, 60% boys, 40% girls. 20% of boys and 30% of girls study science. Find total science students.

14.11.2 Set B – Advanced

  1. In a pie chart, two sectors are 108° and 72°. Ratio of their values?
  2. From a line graph, exports rise from 250 to 400 in 4 years. Average annual growth?
  3. Mixed graph: Table shows cost, line shows revenue. For year X, revenue=500, cost=400. Find profit%.
  4. A bar graph shows income=200, expenditure=150, 180, 170 for 3 years. Which year has highest savings?
  5. A caselet: Out of 600 employees, 40% in sales, 30% in admin, rest in production. If 20% of admin are women and 25% of production are women, find total women if 40% of sales are women.

14.12 Summary

  • DI = arithmetic applied to visual/tabular data.
  • Core tools: % change, ratios, averages.
  • Different formats: table, bar, line, pie, caselet, mixed.
  • Strategy: Read carefully, note base, avoid calculation traps.
  • Practice improves speed; use approximation for time efficiency.