31 Graphical representation (Bar-chart, Histograms, Pie-chart, Table-chart and Line-chart) and mapping of Data
31.1 What the Syllabus Covers
The syllabus names five chart families — Bar-chart, Histogram, Pie-chart, Table-chart, Line-chart — plus the mapping of data (geographical/thematic maps). PYQ patterns: (a) name the chart suited to a given data type, (b) distinguish bar chart vs histogram, (c) interpret a pie chart by computing degrees, (d) read ogive/histogram/Lorenz curves, and (e) recognise thematic map types (choropleth, dot, isopleth, flow).
31.2 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.
- Comparison — across categories or time.
- Distribution — shape, spread, outliers.
- Composition — parts of a whole.
- Relationship — correlation, trend.
- Geographic / spatial — variation across regions.
31.3 Bar Chart
A bar chart uses rectangular bars of equal width whose length (vertical) or height (horizontal) is proportional to the value represented. Bars are separated by gaps — because data are categorical.
| Variant | What it shows |
|---|---|
| Simple bar chart | One variable per category |
| Multiple / grouped bar chart | Two or more series compared per category |
| Stacked bar chart | Parts of a whole within each category |
| Percentage stacked bar | All stacks normalised to 100 % |
| Horizontal bar chart | When category names are long |
| Bilateral / two-directional bar | Positive and negative values (gains/losses) |
31.3.1 Best For
Comparing discrete categories — countries, products, time periods, departments.
31.3.2 Pareto Chart
A special bar chart ordered by descending magnitude, often with a cumulative percentage line — used in quality management to identify the “vital few” causes (Vilfredo Pareto, 80/20 principle).
31.4 Histogram
A histogram is a bar chart for continuous quantitative data organised into class intervals. Bars touch because the x-axis is a continuous scale.
- X-axis: continuous variable (e.g., marks).
- Y-axis: frequency (or relative frequency, or density).
- Bars touch — no gaps.
- Area of each bar ∝ class frequency (in a density histogram).
- Unequal class widths require area adjustment to keep proportionality.
- Frequency polygon — joining midpoints of histogram bars.
- Frequency curve — smoothed frequency polygon.
31.4.1 Histogram vs Bar Chart — The Single Most Asked PYQ
| Feature | Histogram | Bar Chart |
|---|---|---|
| Data type | Continuous quantitative | Categorical |
| X-axis | Numeric scale (intervals) | Categories |
| Bars | Touch (no gaps) | Have gaps |
| Width meaning | Class interval width | Arbitrary (cosmetic) |
| Bar order | Fixed by x-axis values | Re-orderable |
31.4.2 Ogive (Cumulative Frequency Curve)
- “Less than” ogive — cumulative frequency below each upper class limit; rises from left.
- “More than” ogive — cumulative frequency above each lower limit; falls from left.
- The two curves intersect at the median.
- Quartiles, percentiles, and median are read off the ogive directly.
31.5 Pie Chart
A pie chart uses a circle divided into sectors whose central angles are proportional to the values they represent.
- Total = 360°.
- Sector angle = (value / total) × 360°.
- Percent for sector = (value / total) × 100.
- From angle to % = (angle / 360) × 100.
31.5.1 Pie-Chart Variants
- Simple pie — one whole divided into parts.
- Doughnut chart — pie with hole in the middle.
- 3-D pie — discouraged (distorts perception).
- Exploded pie — one slice pulled out for emphasis.
- Pie of pie / Bar of pie — small sectors expanded into a second chart.
31.5.2 When NOT to Use a Pie
- More than 5-7 categories — eye cannot compare many slice sizes.
- Time-series — use a line chart.
- Comparing two pies of the same composition — use stacked bars instead.
31.5.3 Worked Example
Family monthly budget: Food ₹15,000 · Rent ₹10,000 · Transport ₹5,000 · Savings ₹6,000 · Other ₹4,000. Total = ₹40,000. - Food angle = (15000/40000) × 360 = 135°. - Rent angle = (10000/40000) × 360 = 90°. - Transport angle = (5000/40000) × 360 = 45°. - Savings angle = (6000/40000) × 360 = 54°. - Other angle = (4000/40000) × 360 = 36°. - Sum check: 135+90+45+54+36 = 360° ✓.
31.6 Line Chart / Line Graph
A line chart plots data points connected by line segments. Best for trends over time — typically a time-series.
- Simple line — one series.
- Multiple line — several series compared.
- Stacked line / area chart — running totals; parts of a whole over time.
- Smoothed / spline curve.
- Step chart — values change at discrete points.
- Slope chart — comparing two time points only.
31.6.1 When to Use a Line Chart
For continuous time-series, trend visualisation, and rate of change. Not for categorical comparisons (use bar) or composition (use pie or stacked bar).
31.7 Table-Chart
A table-chart (often just “table”) presents structured numerical data in rows and columns. It is the most precise form of data presentation — the only one that retains exact values.
- Table number · 2. Title · 3. Head-note · 4. Stub (row labels) · 5. Caption (column labels) · 6. Body · 7. Source note · 8. Footnote.
31.7.1 Table Types
Simple (one-way) · Two-way · Manifold (multi-way) · Reference (general) · Summary (derived measures) · Frequency table (distribution).
31.8 Other Important Charts
31.8.1 Distribution Charts
- Histogram — frequency by interval.
- Frequency polygon / curve.
- Box plot / Box-and-whisker plot (Tukey 1977) — shows median, quartiles, IQR, outliers.
- Violin plot — box plot with density shape.
- Stem-and-leaf plot — Tukey EDA.
- Dot plot — for small datasets.
31.8.2 Relationship Charts
- Scatter plot — bivariate continuous; correlation pattern.
- Bubble chart — scatter with size encoding a third variable.
- Heat map — correlation matrix, or grid of values.
- Hexbin plot — high-density scatter.
31.8.3 Composition Charts
- Pie / doughnut chart.
- Stacked / 100 % stacked bar.
- Treemap — nested rectangles proportional to value (Ben Shneiderman, 1991).
- Sunburst chart — radial treemap.
- Waterfall chart — sequential gains/losses.
- Mosaic plot.
31.8.4 Inequality and Concentration
- Lorenz curve (Max Lorenz, 1905) — cumulative share of population vs cumulative share of income/wealth.
- Line of equality = 45° line (perfect equality).
- Gini coefficient = ratio of the area between line of equality and Lorenz curve to the total triangle area below the equality line. Gini = 0 (perfect equality) to 1 (perfect inequality).
31.8.5 Time-Series
- Line chart (most common).
- Area chart.
- Sparkline (Tufte) — small inline trend line.
- Candlestick — financial.
- Z-chart — sales monthly + cumulative + 12-month rolling.
31.9 Mapping of Data — Cartograms
Mapping data on geography uses thematic maps.
| Map Type | What it shows | Example |
|---|---|---|
| Choropleth | Colour-coded regions by value | State-wise literacy in India |
| Dot density | One dot per N units | Population dots |
| Isopleth / Isarithmic | Contours of equal value | Rainfall isohyets |
| Flow map | Movement (arrows) | Migration, trade flows |
| Proportional symbol | Symbol size by value | City population circles |
| Heat map (geographic) | Continuous colour intensity | Crime hotspots |
| Cartogram | Area distorted by data | GDP cartogram of India |
| Dasymetric | Refined choropleth with secondary data | Population density |
| Pin map | Markers at point locations | Disease cases |
31.9.1 GIS — Geographic Information System
- Open-source: QGIS, GRASS GIS, GeoServer.
- Commercial: ArcGIS (Esri), MapInfo.
- Indian platforms: Bhuvan (ISRO) — Indian geospatial portal; NRSC (National Remote Sensing Centre); Survey of India.
- Web-mapping: Google Maps, OpenStreetMap, Mapbox, Leaflet.
31.10 Designing Good Charts — Principles
Edward Tufte, The Visual Display of Quantitative Information (1983): 1. Show the data above all. 2. Maximise data-ink ratio — minimise non-data ink (gridlines, decoration). 3. Avoid chartjunk — useless 3-D, frames, textures. 4. Use small multiples — many small panels comparing variants. 5. High data-density. 6. Lie factor near 1 — graph proportions ≈ data proportions.
Order (most accurate first): Position on common scale → Position on non-aligned scale → Length → Direction/Angle → Area → Volume → Colour saturation / hue.
Implication: bar charts (position) read more accurately than pie charts (angle).
31.11 Choosing the Right Chart — A Decision Cheat-Sheet
| If you want to show… | Use |
|---|---|
| Compare categories | Bar chart |
| Distribution of continuous variable | Histogram, box plot |
| Composition of one whole | Pie / stacked bar (small categories only) |
| Composition over time | Stacked area |
| Trend over time | Line chart |
| Two continuous variables | Scatter plot |
| Three or four variables | Bubble / heatmap |
| Geographic variation | Choropleth, isopleth |
| Hierarchical breakdown | Treemap / sunburst |
| Inequality | Lorenz curve / Gini |
| Cumulative gain/loss | Waterfall chart |
| Outliers + spread | Box plot, violin plot |
31.12 Theory Anchors
| Person | Year | Contribution |
|---|---|---|
| William Playfair | 1786, 1801 | Invented line, bar, area, pie charts |
| Florence Nightingale | 1858 | Polar/Coxcomb chart; statistical visualisation as advocacy |
| John Snow | 1854 | Cholera dot map of London — foundational thematic mapping |
| Charles Joseph Minard | 1869 | Napoleon’s Russian campaign flow map — Tufte’s “best graph ever” |
| Max Lorenz | 1905 | Lorenz curve |
| Karl Pearson | early 20th c. | Histogram (term coined 1891) |
| Vilfredo Pareto | 1896 | 80/20 principle; Pareto chart |
| John W. Tukey | 1977 | Box plot; Exploratory Data Analysis (EDA) |
| Jacques Bertin | 1967 | Semiology of Graphics — visual variables |
| William Cleveland & McGill | 1984 | Perceptual accuracy ranking |
| Edward Tufte | 1983 | Visual Display of Quantitative Information; data-ink ratio |
| Ben Shneiderman | 1991 | Treemap |
| Hans Rosling | 2010s | Gapminder; animated bubble charts |
31.13 Practice Questions
The single most important visual difference between a histogram and a bar chart is:
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A category contributing 30 % of the total in a pie chart corresponds to a central angle of:
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To show monthly sales over five years, the BEST chart is:
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The "less-than" and "more-than" ogives of a frequency distribution intersect at:
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A Pareto chart is a bar chart ordered by:
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The Lorenz curve is used to visualise:
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A map colour-coding Indian states by literacy rate is a:
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Contour lines of equal rainfall on a map are called:
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A scatter plot is BEST for showing:
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The box-and-whisker plot was popularised by:
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The line, bar, and pie charts were invented by:
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The "data-ink ratio" — maximising the proportion of ink devoted to data — was advocated by:
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The 1854 dot map of cholera cases in London — foundational in epidemiology and thematic mapping — was produced by:
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According to Cleveland and McGill (1984), the MOST accurate visual encoding for quantitative comparison is:
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A map in which the areas of regions are distorted to be proportional to a data value (e.g., GDP) is called:
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India's geospatial portal "Bhuvan" is developed by:
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A "treemap", showing hierarchical data as nested rectangles proportional to value, was invented in 1991 by:
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The polar-area / coxcomb diagram used in 1858 to advocate for sanitary reform in the British Army was popularised by:
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To compare the relative shares of five product categories of a company's sales, the BEST chart is:
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Match each chart with its primary purpose:
| (i) | Histogram | (a) | Trend over time |
| (ii) | Line chart | (b) | Inequality |
| (iii) | Choropleth | (c) | Distribution of continuous variable |
| (iv) | Lorenz curve | (d) | Geographic variation |
View solution
31.14 Quick Recall
- Why graphs > tables: patterns visible. Tables = precise values.
- 5 functions of charts: Comparison · Distribution · Composition · Relationship · Geographic.
- Bar chart: categorical x-axis, bars have gaps. Variants: simple, grouped, stacked, percent-stacked, horizontal, bilateral. Pareto chart = descending magnitude + cumulative line.
- Histogram: continuous x-axis, bars touch. Area ∝ frequency. Frequency polygon = joining midpoints. Frequency curve = smoothed polygon.
- Histogram vs bar: touch vs gap; continuous vs categorical.
- Ogive: cumulative frequency curve. Less-than rises; more-than falls. Intersect at median.
- Pie chart: 360° total. Sector angle = (value/total) × 360°. Avoid >5-7 slices, time-series, 3-D.
- Line chart: trend over time. Variants: simple, multiple, stacked area, smoothed/spline, step, slope.
- Table-chart parts (8): number · title · head-note · stub (rows) · caption (columns) · body · source · footnote.
- Distribution charts: histogram · frequency polygon · box plot (Tukey 1977) · violin · stem-and-leaf · dot.
- Relationship charts: scatter · bubble · heatmap · hexbin.
- Composition charts: pie · stacked bar · treemap (Shneiderman 1991) · sunburst · waterfall · mosaic.
- Inequality: Lorenz curve (Lorenz 1905) · Gini coefficient (0–1).
- Time-series: line · area · sparkline (Tufte) · candlestick · Z-chart.
- Map types: Choropleth (colour by value), Dot density, Isopleth/Isarithmic (contours: isohyets/isobars/isotherms), Flow, Proportional symbol, Heat map, Cartogram (distorted area), Dasymetric, Pin map.
- Indian GIS: Bhuvan (ISRO), NRSC, Survey of India. Web maps: Google Maps, OSM, Mapbox, Leaflet. Open GIS: QGIS.
- Tufte (1983): data-ink ratio · avoid chartjunk · small multiples · lie factor.
- Cleveland & McGill (1984) accuracy order: Position on common scale > non-aligned position > length > angle > area > volume > colour. Bars beat pies.
- History: Playfair (line, bar, pie 1786/1801) · Snow (cholera dot map 1854) · Nightingale (coxcomb 1858) · Minard (Napoleon 1869) · Lorenz (1905) · Pearson (histogram, 1891) · Tukey (1977) · Bertin (1967) · Tufte (1983) · Shneiderman (treemap 1991) · Rosling (Gapminder).