30  Graphical Representation and Mapping of Data

A graph is a visual encoding of data that allows quick perception of pattern, magnitude and relationship. Different chart types are suited to different data types and questions.

30.1 Why Graphs Beat Tables

A table presents exact values; a graph presents patterns. Tables are best for precise look-up; graphs are best for comparing magnitudes, spotting trends, and seeing distribution.

TipThree Working Principles of Good Graphs (Tufte 1983)
  1. Show the data — minimise non-data ink.
  2. Avoid distortion — proportions in the graph must match proportions in the data.
  3. Reveal at multiple levels of detail — overall shape and individual values.

30.2 Common Chart Types and When to Use Them

TipWorking Chart Types
Chart What it shows When to use
Bar chart Comparison of values across categories Categorical x, numeric y
Column chart Same as bar chart, vertical Same
Pie chart Parts of a whole Few (≤ 5) categories that sum to 100 %
Line chart Trend over time Continuous x (time), numeric y
Histogram Distribution of a continuous variable Single continuous variable; bars touch
Frequency polygon Same as histogram, drawn as line Compare distributions
Ogive Cumulative frequency Find median, quartiles
Scatter plot Relationship between two numeric variables Correlation, regression
Box plot Distribution summary (median, quartiles, outliers) Compare distributions across groups
Stacked bar / column Composition across categories Each bar split into components
Pictogram Icon-based comparison Mass communication, public reports
Heatmap Two-dimensional intensity Correlation matrix, time × category
Choropleth map Geographic intensity Region-level data on a map
Bubble chart Three numeric variables (x, y, size) Wealth × population × GDP 

flowchart TB
  G[Graph] --> CT[Categorical Comparison]
  G --> TR[Trend over Time]
  G --> DT[Distribution]
  G --> RL[Relationship]
  G --> GE[Geographic]
  CT --> B[Bar / Column]
  CT --> P[Pie]
  TR --> L[Line]
  DT --> H[Histogram]
  DT --> BP[Box plot]
  RL --> SC[Scatter]
  RL --> HM[Heatmap]
  GE --> CH[Choropleth map]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

30.3 Bar Chart vs Histogram — A Frequent NTA Distractor

TipBar Chart vs Histogram
Feature Bar Chart Histogram
Variable on x-axis Categorical Continuous (numeric)
Bars Have gaps between them No gaps; bars touch
Order of bars Arbitrary or alphabetical Determined by numerical order
Use Comparing categories Showing frequency distribution
Width meaning Width has no meaning Width = class interval

30.4 Pie Chart Fundamentals

A pie chart represents a whole divided into parts. Each slice’s angle is proportional to the part’s percentage.

TipPie Chart — Angle Calculation

Angle = (Value / Total) × 360°

If a category has 25 % of the total, its slice = (25/100) × 360° = 90°.

TipWorked example

A class of 60 students consists of 24 in Arts, 18 in Science, 12 in Commerce, 6 in Engineering.

  • Arts: (24/60) × 360 = 144°
  • Science: (18/60) × 360 = 108°
  • Commerce: (12/60) × 360 = 72°
  • Engineering: (6/60) × 360 = 36°

Total = 360° ✓

30.5 Box Plot

A box plot (introduced by John Tukey, 1977) displays the five-number summary of a distribution.

TipFive-Number Summary
  1. Minimum — smallest value (or lower whisker)
  2. Q1 — 25th percentile (lower edge of box)
  3. Median (Q2) — 50th percentile (line inside box)
  4. Q3 — 75th percentile (upper edge of box)
  5. Maximum — largest value (or upper whisker)

The interquartile range (IQR) = Q3 − Q1 measures the spread of the middle 50 % of data. Points outside Q1 − 1.5 × IQR or Q3 + 1.5 × IQR are typically marked as outliers.

30.6 Scatter Plot and Correlation

A scatter plot reveals the relationship between two numerical variables.

TipReading a Scatter Plot
Pattern Interpretation
Points form a rising line Positive correlation
Points form a falling line Negative correlation
Points scattered randomly No correlation
Points form a curve Non-linear relationship
Cluster + outliers Outliers warrant inspection

The correlation coefficient (r) ranges from −1 (perfect negative) to +1 (perfect positive); 0 = no linear relationship.

30.7 Mapping Data — Geographic Visualisation

TipThree Common Map Types
Map type What it shows Example
Choropleth map Region shaded by intensity of a variable District-level literacy rate
Dot density map Each dot = N units of a quantity Population by district
Proportional symbol map Symbol size scaled to magnitude City population by circle size

30.8 Choosing the Right Chart

TipFive Working Questions for Choosing a Chart
  1. What is the data type? — Numeric, categorical, mixed.
  2. What is the question? — Comparison, trend, distribution, relationship, composition, geography.
  3. How many variables? — One (univariate), two (bivariate), three or more (multivariate).
  4. How many data points? — Few (table or bar) or many (histogram, scatter, heatmap).
  5. Audience? — Technical (box plot, scatter) or general (pie, pictogram).

30.9 Common Mistakes in Chart Design

TipFive Frequent Mistakes
Mistake What it does
Truncated y-axis Exaggerates differences; the axis should usually start at zero for bar charts
3-D effects Distort area perception; flat is more accurate
Pie chart with too many slices Hard to compare angles; use a bar chart instead
Using line chart for categorical x Implies continuous progression where there isn’t one
Multiple overlaid lines without colour distinction Cannot read individual series

30.10 Practice Questions

Q 01 Pie Chart Easy

If a category accounts for 25 % of the total in a pie chart, the angle of its slice is:

  • A25°
  • B90°
  • C120°
  • D180°
View solution
Correct Option: B
Angle = (% / 100) × 360° = (25/100) × 360 = 90°.
Q 02 Histogram vs Bar Medium

The defining feature of a histogram (compared to a bar chart) is that:

  • ABars are vertical
  • BBars touch each other (no gaps), and the x-axis is continuous
  • CIt uses three dimensions
  • DIt can only show ordinal data
View solution
Correct Option: B
A histogram shows continuous data; bars touch because the x-axis is a number line. Bar charts show categories and bars have gaps.
Q 03 Box Plot Medium

A box plot displays which of the following five-number summary?

  • AMean, mode, median, range, SD
  • BMinimum, Q1, median, Q3, maximum
  • CSum, count, mean, median, mode
  • DFirst, last, average, minimum, maximum
View solution
Correct Option: B
The five-number summary is Min, Q1, Median (Q2), Q3, Max.
Q 04 Scatter Plot Easy

A scatter plot is most appropriate for visualising:

  • AA trend over time
  • BThe relationship between two numeric variables
  • CParts of a whole
  • DGeographic distribution
View solution
Correct Option: B
Scatter plots reveal the relationship between two numerical variables.
Q 05 Choropleth Medium

A *choropleth map* shades regions according to the magnitude of a variable. Which of the following is best displayed using a choropleth map?

  • ADaily stock prices over a month
  • BDistrict-wise literacy rate across India
  • CDistribution of student grades
  • DComparison of two textbook prices
View solution
Correct Option: B
A choropleth works for region-level intensity — district-wise literacy rate is a perfect example.
Q 06 Pie Chart Calc Medium

In a pie chart of a household monthly budget of ₹40,000, the slice representing food has an angle of 108°. The food budget is:

  • A₹10,000
  • B₹12,000
  • C₹14,000
  • D₹16,000
View solution
Correct Option: B
Food % = (108/360) × 100 = 30 %. Food budget = 30 % of 40,000 = ₹12,000.
Q 07 Correlation Medium

A correlation coefficient of −0.85 indicates:

  • AStrong positive correlation
  • BStrong negative correlation
  • CNo correlation
  • DCausation
View solution
Correct Option: B
|r| close to 1 = strong; negative sign = inverse direction → strong negative correlation. Correlation does not imply causation.
Q 08 Chart Choice Hard

Match the visualisation question with the most appropriate chart type:

(i) Compare values across 5 categories (a) Histogram
(ii) Show distribution of a continuous variable (b) Line chart
(iii) Show trend over 12 months (c) Bar chart
(iv) Compare two distributions side by side (d) Box plot
  • A(i)-(c), (ii)-(a), (iii)-(b), (iv)-(d)
  • B(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
  • C(i)-(b), (ii)-(c), (iii)-(d), (iv)-(a)
  • D(i)-(d), (ii)-(c), (iii)-(b), (iv)-(a)
View solution
Correct Option: A
Compare categories → bar; distribution → histogram; trend over time → line; compare distributions → box plot.
ImportantQuick recall
  • Bar chart for categorical comparison; histogram for continuous distribution (bars touch).
  • Pie chart angle = (value/total) × 360°.
  • Box plot = 5-number summary: Min, Q1, Median, Q3, Max. IQR = Q3 − Q1.
  • Scatter plot for relationship between two numeric variables; r ranges −1 to +1.
  • Choropleth for region-level data on a map.
  • Common mistakes: truncated y-axis, 3-D pies, pies with too many slices, line chart for categorical x.