Graphical Representation of Data and Thematic Maps

1. Representing data: purpose and general rules

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• Representation of data means turning data into visual forms: graphs, diagrams, maps and charts. The pattern is then seen at a glance and remembered longer. The method must suit the nature of the data.
• Why bother: Class 12, Graphical Representation of Data says the Nagpur district maps (Class 11, Introduction to Maps) would lose their visual impact as tables or text, and would take longer to read. In its words, "a picture is equivalent to thousands of words." Visual forms make comparison easy. They show patterns of population growth, density, sex ratio, age-sex make-up and occupations.
• Three general rules:
• Suitable method: line graph for temperature or population growth over time; bar diagram for rainfall or production; dot map for population, livestock or crop distribution; choropleth for population density.
• Suitable scale: it must cover all the data and be neither too large nor too small.

• Design: a title (area, subject, reference year) centred at the top; a legend explaining colours, shades and symbols, usually lower left or lower right; a north arrow on maps (design detail: maps-and-scale).

• Diagrams by dimension:

Type	Examples
One-dimensional	line graph, polygraph, bar diagram, histogram, age-sex pyramid
Two-dimensional	pie diagram, rectangular diagram
Three-dimensional	cubes, spheres

• NCERT covers only the commonest: line graphs, bar diagrams, the pie diagram, the wind rose and star diagram (named only) and flow charts.

2. Line graphs and polygraphs

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• A line graph joins plotted points with a line. Time goes on the X-axis. It is best for time-series data (data recorded over time): temperature, rainfall, population growth, birth and death rates.
• Steps: round off the data → put time on the X-axis and values on the Y-axis → choose a scale that includes negative values if there are any → plot the points and join them freehand.
• NCERT example (Table 3.1, Fig. 3.2): India's annual population growth rate. It was 0.56% in 1911. In 1921 it was −0.30%, the only negative decade. It peaked at 2.20–2.22% in 1971–81 and fell to 1.79% in 2011 (NCERT figure; Census 2011 gives 1.64% a year for 2001–11, verify current).
• Why 1911–21 fell (beyond NCERT): the 1918 influenza pandemic, famines and epidemics. 1921 is called the "great divide" in India's population history (pointer india-population).
• A polygraph is a line graph with two or more lines. Each line has its own style (solid, broken, dotted, dot-dash) or colour, so several variables can be compared at once.
• NCERT example (Table 3.2, Fig. 3.3): sex ratio (females per 1,000 males) of Delhi, Haryana and Uttar Pradesh, 1961–2011. Delhi rose from 785 (1961) to 866 (2011).
• Trap: NCERT's answer is that a polygraph shows "more than two variables", not "two variables only".

3. Bar diagrams, the line-and-bar graph and the histogram

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• A bar diagram (columnar diagram) uses bars of equal width at equal spacing. Bar length is proportional to the value. Bars are shaded or coloured to tell them apart.
• Simple bar diagram: one bar per item, for quick comparison. Arrange the bars in ascending or descending order, but keep time series in time order. NCERT example: monthly rainfall of Thiruvananthapuram, with a June peak of 35.6 cm (Table 3.3, Fig. 3.4).
• Multiple bar diagram: adjoining bars, one for each variable, for each item. NCERT example: total, male and female literacy went from 18.33, 27.16 and 8.86% in 1951 to 73.0, 80.9 and 64.6% in 2011 (Census 2011; Table 3.5).
• Compound bar diagram: one bar for the total, split into rectangles for its parts. NCERT example: gross electricity generation (thermal, hydro, nuclear) grew from 741.2 billion kWh in 2008-09 to 844.8 billion kWh in 2010-11 (Economic Survey 2011-12; Table 3.6).
• Line and bar graph: both shapes on shared months. Rainfall is shown as bars on one Y-axis and temperature as a line on the other. NCERT example: Delhi, with temperature from 14.4°C in January to 33.3°C in May–June and rainfall peaking at 19.3 cm in July (Table 3.4). It is the standard way to show a station's climate (exercise: Kolkata).
• Histogram: adjoining bars with no gaps. Bar widths are the class intervals and heights (strictly, areas) are the frequencies, so it shows continuous data. A bar diagram has gaps and shows separate categories. Joining the midpoints of the bar tops gives the frequency polygon (pointer geographical-data-processing).

4. Pie diagrams and wind roses

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• A pie diagram (divided circle diagram) shows a total as a circle. The circle is cut into sectors in proportion to the parts.
• Angle formula: angle = (value of part ÷ total) × 360, or percentage × 3.6.
• NCERT example, India's exports by region in 2010-11 (Economic Survey 2011-12; Table 3.7):

Region	%	Angle
Asia and ASEAN	56.2	203°
Europe	20.2	73°
America	14.8	53°
Africa	6.5	23°
Others	2.3	8°

• Steps: choose a radius of 3–5 cm → draw one radius line → measure the angles clockwise, starting with the smallest → add title, subtitle and legend. If you start with the biggest angle, errors build up and the small angles become hard to plot. NCERT's steps say "vehicles", but the data are exports (a slip).
• Beyond NCERT: to compare two totals, draw circles of different size, with the radius proportional to the square root of each total. Pies fail when there are many small categories.
• A wind rose shows how often (and often how strongly) winds blow from each direction over a period. It is drawn as bars radiating from a centre toward the directions the winds come from. A star diagram is a similar radial chart for directional or cyclical data, such as monthly values. Uses: aligning airport runways, siting polluting industries downwind of towns.

5. Specialised diagrams: climographs, pyramids, Lorenz curves and ternary diagrams

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All beyond NCERT, but common in geography and economics answers.

• Climograph (Griffith Taylor): monthly wet-bulb temperature plotted against relative humidity. Its cousin, the hythergraph, plots monthly temperature against rainfall. The 12 joined points make a shape typical of each climate: a tight cluster for equatorial climates, a long narrow loop for monsoon climates.
• Population pyramid: paired horizontal bars showing the share of males and females in each age group.
• A wide base means high fertility (Bihar).

• A narrow base and a wider top mean an ageing population (Kerala, Japan). Substance: india-population.

• Lorenz curve: the cumulative share of people or areas is plotted against the cumulative share of a quantity (income, land, industrial output). The more the curve bows away from the diagonal line of equality, the greater the inequality. The Gini coefficient is the area of that gap divided by the area under the diagonal: 0 means perfect equality and 1 means total concentration (pointer human-development).

• Ternary diagram: a triangle for three parts that add up to 100%. Examples: sand, silt and clay in the soil texture triangle (pointer soils-of-india); a workforce split among the primary, secondary and tertiary sectors.

6. Flow maps

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• A flow map (flow chart) is a mix of graph and map. It shows goods, people or vehicles moving between an origin and a destination. Bands are drawn with widths proportional to volume. NCERT calls it a "dynamic map".
• Two kinds of data:
• the number and frequency of vehicles by direction of movement

• the number of passengers or the quantity of goods carried

• Requirements: a route map with stations; flow data with origins and destinations; a scale for line width.

• NCERT example, Delhi trains (Table 3.8, Fig. 3.9–3.10): routes range from 50 trains (Old Delhi–New Delhi) to 6 (Udyog Nagar–Tikri Kalan). At 1 cm = 50 trains, the bands are 10 mm and 1.2 mm thick. A terraced scale (a stepped key of band widths) serves as the legend, with symbols for the nodal stations.
• NCERT example, Ganga basin water flow: 1 cm band width = 50,000 cusecs (Fig. 3.11–3.12).
• Beyond NCERT: flow maps of migration (Census), trade (pointer world-trade, india-international-trade) and commuting. Desire-line maps show straight origin-to-destination links instead of actual routes.

7. Thematic maps: requirements, rules and classes

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• Graphs and diagrams compare values but give no regional perspective. A thematic map (distribution map) shows the spatial pattern of one or a few themes, such as population density, rainfall or literacy, over a base map. Class 6, Locating Places on the Earth calls these maps with one specific kind of information.
• Requirements:
• state or district data on the theme
• an outline map with administrative boundaries

• a physical map of the region: physiography for population, relief and drainage for transport

• Rules: show the area's name, the subject's title, the data source and year, the symbols and shades used, and the scale. Then choose a suitable method.

• Classification by method of construction:

Class	Shows	Example
Quantitative map (statistical)	measurable variations	rainfall >200 cm, 100–200 cm, 50–100 cm, <50 cm
Qualitative map (non-quantitative)	characteristics that cannot be measured	just "high" and "low" rainfall areas; land use types

• NCERT constructs three quantitative types: dot, choropleth and isopleth maps.

8. Dot maps and proportional symbol maps

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• A dot map shows the distribution of counts (population, cattle, crops). Dots of equal size and fixed value are placed inside each administrative unit.
• Requirements: an administrative map; data for each unit; a dot value; a physiographic (relief and drainage) map.
• Steps:
• Fix the dot size and value (1 dot = 1 lakh people in Table 3.9, Census 2001).
• Work out the dots for each unit. Maharashtra: 9,67,52,247 ÷ 1,00,000 = 967.52, rounded up to 968 because the fraction is more than 0.5.

• Place the dots, putting fewer in mountains, deserts and snowfields.

• Precautions: keep boundary lines thin; make all dots the same size.

• Strength: it shows real clustering, for example along rivers and plains.
• NCERT error: Mizoram's 891,058 people get 89 dots in Table 3.9. The correct number is 9.
• Trap: population distribution needs a dot map; population density needs a choropleth.
• A proportional symbol map (beyond NCERT) draws circles, squares or spheres at points in sizes proportional to the quantity, for example city populations or port traffic. The symbol's area, not its radius, should match the value. So the radius is proportional to the square root of the value (cube root for spheres). It suits point data where dots would crowd.

9. Choropleth maps, dasymetric maps and cartograms

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• A choropleth map shades administrative units in graded tones according to an average or ratio per unit: density, literacy, growth rate, sex ratio.
• Steps:
• Arrange the data in order.
• Range = maximum − minimum; class interval = range ÷ 5.

• Make five classes, from very low to very high, and shade them from light to dark.

• NCERT example, literacy (Census 2001; Table 3.10, Fig. 3.14): values run from Bihar 47.0% to Kerala 90.9%. Range = 44, interval ≈ 9, classes 47–56, 56–65, 65–74, 74–83 and 83–92. Mizoram (88.8%) and Kerala are "very high". NCERT's class lists leave out several UTs; Lakshadweep (86.7%) also falls in "very high".

• Rule: use ratios, not absolute counts. Otherwise large units look "high" just because they are large.
• Limits (beyond NCERT):
• The map implies the same value everywhere inside a unit, with a sudden jump at its boundary.
• Large but thinly peopled units dominate the eye.

• The way classes are chosen (equal interval, quantiles, natural breaks) can change the story the map tells.

• Remedies:

• A dasymetric map redraws the zones using extra information, for example removing forests, deserts and water bodies before shading density, so values sit where people actually live.
• A cartogram resizes units in proportion to a variable such as population or GDP. On a population cartogram, India and China swell and Russia and Canada shrink. Election-result maps often use cartograms.

10. Isopleth maps and interpolation

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• Some data change smoothly across space and ignore administrative boundaries: slope, temperature, rainfall, pressure. They are shown by isopleths, lines joining places of equal value. Iso means equal; NCERT glosses pleth as "lines" (the Greek root actually means quantity).

Isopleth	Joins equal…
Isotherm	temperature
Isobar	pressure
Isohyet	rainfall over a set period
Isoneph	cloudiness
Isohel	sunshine
Contour	height
Isobath	depth below a water surface (sea-floor relief)
Isohaline	salinity of sea water
Isoseismal*	earthquake intensity
Isochrone*	travel time
Isogonic line*	magnetic declination

*beyond NCERT

• Requirements: a base map with point locations; values for a fixed period; drawing instruments (a French curve).
• Rules: use equal intervals (5, 10 or 20 is ideal). Write each line's value along it, on one side or in a break in the line.
• Interpolation means estimating values between observed points in proportion to distance. Position of the isopleth = (distance between the two points ÷ difference between their values) × interval.
• NCERT example: stations at 28°C and 33°C are 10 mm apart. The 30°C isotherm falls (10 ÷ 5) × 2 = 4 mm from the 28°C station. Draw the lowest-value isopleth first (Fig. 3.15).
• Beyond NCERT: GIS interpolation methods (inverse distance weighting, kriging) turn rain-gauge and weather-station readings into IMD's gridded rainfall and temperature maps.

11. Choosing the right diagram or map

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Diagrams: match the data to the method

Data	Best method
Time series, one variable	line graph
Time series, several variables	polygraph
Comparison of items	simple bar
Several variables per item	multiple bar
Parts of a total	compound bar or pie (pie for one total's shares)
Frequency distribution / cumulative distribution	histogram or frequency polygon / ogive
Climate of a station	line and bar graph, climograph
Wind directions	wind rose
Age-sex structure / inequality / three-part mix	pyramid / Lorenz curve / ternary diagram

Maps:

• absolute counts → dot map (proportional symbols for point data)
• ratios per unit → choropleth (refined by a dasymetric map)
• continuous surfaces → isopleths
• movements → flow map
• size-based comparison → cartogram

NCERT's exercises show the pattern: population distribution = dot map; decadal growth = line graph; "dynamic map" = flow map; land use shares in 1950-51 vs 1998-2001 = two pie diagrams; rice area by state = multiple bar; share of rice output = choropleth. Today these are made with GIS and spreadsheet software (pointer remote-sensing-gis), but the logic of choice is the same.

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Exam angles

Prelims — high-yield facts and traps

• Isoline pairs: isohyet = rainfall; isohaline = salinity; isobath = depth; isoneph = cloudiness; isohel = sunshine; isobar = pressure; isotherm = temperature; isoseismal = earthquake intensity; contour = height.
• Dot map = distribution of counts. Choropleth = density or ratios by administrative unit. Isopleth = continuous data, drawn regardless of boundaries.
• "Choropleth for population distribution" is FALSE; distribution uses a dot map.
• Flow map = "dynamic map"; band width is proportional to volume.
• Pie angle = percentage × 3.6. Draw clockwise starting from the smallest angle.
• Polygraph = more than two variables. "Two variables only" is FALSE.
• Compound bar = parts inside one bar. Multiple bar = adjoining bars per item.
• Histogram = adjoining bars for continuous classes. Bar diagram = gaps between separate categories.
• In NCERT's choropleth method, class interval = range ÷ 5, giving five classes.
• Proportional symbols: the symbol's area, not its radius, is proportional to the value.
• Lorenz curve: the further it bows from the diagonal, the greater the inequality. Gini ranges from 0 (equal) to 1 (concentrated).
• Interpolation: 28°C and 33°C stations 10 mm apart put the 30°C isotherm 4 mm from 28°C.

Mains — GS-I themes

1. "The choice of a cartographic method depends on the nature of data." Illustrate with dot, choropleth and isopleth maps.
2. Limits of choropleth maps for showing population, and how dasymetric maps and cartograms fix them.
3. Thematic maps and diagrams in regional planning and policy: literacy gaps, sex ratio, rainfall variability, migration flows.
4. Data visualisation and public understanding: how maps can inform or mislead (election maps, pandemic dashboards).

Current-affairs hooks

• Official dashboards and atlases that use choropleth and flow maps: Census, NFHS district factsheets, IMD rainfall departure maps, migration data (verify current).
• Election-result cartograms and debates on misleading maps.
• IMD's gridded rainfall and temperature products and its heat-wave maps (verify current).
• Government GIS portals (Bhuvan, PM Gati Shakti) publishing thematic layers (pointer remote-sensing-gis).