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சா/த · புவியியல் · தரம் 11 · அலகு 10
1️⃣1️⃣ தரம் 11 · அலகு 10

தரவுகளை விளக்குவதற்காக வரைபுகளைப் பயன்படுத்தல்

Using graphs to interpret data
★★★★☆ வரைபு வகைகள்தரவு விளக்கம்

\"இந்த எண்களை ஒரு கதையாகச் சொல்ல முடியுமா?\" — அதுவே graphs + charts-ன் நோக்கம். Tables of numbers are hard to digest at a glance — but the same data converted to a **graph** (வரைபு) reveals trends, comparisons, patterns instantly. கடைசி அலகாக நாம் — (1) எப்போது எந்த வரைபு பயன்படுத்துவது, (2) Bar charts, line graphs, pie charts, climographs construction, (3) data interpretation, (4) common mistakes — பற்றி அறிவோம்.

உரு 10.1 — Geographic data visualizations: bar, line, pie, climograph, scatter.
உரு 10.1 — Geographic data visualizations: bar, line, pie, climograph, scatter. NIE பாடநூல், தரம் 11

1. Why Visualize Data?

Geography deals with numbers everywhere — populations, rainfall, temperatures, crop yields, export values, GDP. These numbers as tables are hard to compare. Visualizing them as graphs:

  • Reveals trends over time at a glance.
  • Allows quick comparisons across categories.
  • Shows proportions + relationships.
  • Identifies outliers + anomalies.
  • Communicates findings to non-technical audiences.
  • Reveals spatial patterns via maps + cartograms.

2. Choose Right Graph Type

GoalBest GraphExamples
Show trend over timeLine graphPopulation growth, temperature time-series, GDP trend
Compare categoriesBar chart (vertical/horizontal)Population by district, export by commodity
Compare multiple categories over timeMultiple bar / Grouped barImports vs exports per year
Show parts of wholePie chartLand use breakdown, ethnic composition
Compare two related variablesScatter plotRainfall vs crop yield
Climate at a placeClimograph (combined bar + line)Monthly rainfall (bars) + temperature (line)
Spatial dataChoropleth map (shaded)Population density by district
HierarchicalTreemapExport value by commodity nested
Frequency distributionHistogramIncome distribution, rainfall distribution

3. Line Graph (கோட்டு வரைபு)

உரு 10.2 — Simple line graph: data trend over time.
உரு 10.2 — Simple line graph: data trend over time. NIE பாடநூல், தரம் 11

Use

Tracking changes over time. Best for continuous data — temperature, population, GDP, etc.

Construction

  1. Horizontal axis (X) = independent variable, usually time (years).
  2. Vertical axis (Y) = dependent variable being measured.
  3. Use suitable + uniform scale on both axes.
  4. Plot each (x, y) value as a point.
  5. Connect points with smooth line (or straight segments).
  6. Label both axes clearly with units.
  7. Title at top.
  8. Source citation at bottom.
  9. For comparisons, use multiple lines with legend (different colors/styles).

Example: SL Population Growth 1871-2012

X-axis: years (1871, 1881, 1891, ... 2012); Y-axis: population in millions. Single ascending line showing J-curve growth — easy to see acceleration.

Variations

  • Multiple line graph — compare multiple data series. e.g., population growth of SL vs India.
  • Compound line graph — areas filled to show component contributions.
  • Cumulative line — running total over time.

4. Bar Chart (வரிக் கட்டை வரைபு)

உரு 10.3 — Multiple bar chart: categories compared side-by-side.
உரு 10.3 — Multiple bar chart: categories compared side-by-side. NIE பாடநூல், தரம் 11

Use

Comparing discrete categories. Best for nominal or ordinal data — countries, districts, products.

Construction

  1. One axis (usually X) for categories.
  2. Other axis (usually Y) for values.
  3. Draw bars equal width with equal gaps between.
  4. Bar height/length proportional to value.
  5. Label both axes.
  6. Label each bar (category name) clearly.
  7. Title + source.
  8. Order: alphabetical, or by value descending (often most informative).

Variations

  • Simple bar chart — one variable per category.
  • Multiple/Grouped bar — multiple variables per category (e.g., 2020 vs 2024 by district).
  • Stacked bar — total + sub-component breakdown.
  • 100% stacked — show proportional composition.
  • Horizontal bar — long category names readable.
  • Population pyramid — special form showing age-sex structure (two back-to-back bars).

Example: SL Districts by Population

X-axis: district names (Colombo, Gampaha, Kandy, ...); Y-axis: population in thousands. Tallest bar = Colombo. Easily ranked + compared.

5. Pie Chart (வட்ட வரைபு)

உரு 10.4 — Pie chart: proportion of whole shown as slices.
உரு 10.4 — Pie chart: proportion of whole shown as slices. NIE பாடநூல், தரம் 11

Use

Show proportional composition of a whole. Best for few categories (4-7) where sum = 100%.

Construction

  1. Calculate angle for each category: (category value ÷ total) × 360°.
  2. Draw circle.
  3. Use protractor to mark angles + draw radii.
  4. Color/shade each slice differently.
  5. Label each slice with category name + percentage.
  6. Title + source.
  7. Order: largest first (clockwise from 12 o\'clock).

Example: SL Ethnic Composition 2012

Sinhalese 74.9% = 270° angle; SL Tamil 11.2% = 40°; SL Moor 9.2% = 33°; Indian Tamil 4.2% = 15°; Others 0.5% = 2°. Sum = 360°. Visually clear majority + minorities.

When NOT to use

  • Too many categories (>7) — slices too thin.
  • Categories have nearly equal values — hard to distinguish.
  • Show changes over time — line graph better.
  • Show negative values — pie charts cannot.

6. Climograph (காலநிலை வரைபு)

Use

Show a location\'s climate at a glance — monthly rainfall + temperature combined.

Construction

  1. X-axis: 12 months (Jan-Dec).
  2. Left Y-axis: temperature (°C).
  3. Right Y-axis: rainfall (mm).
  4. Plot temperature as line (using left Y-axis).
  5. Plot rainfall as bars (using right Y-axis).
  6. Label axes + title with location.

Example: Nuwara Eliya Climograph

Temperature line: ~13-16°C throughout year (relatively flat — high elevation cool). Rainfall bars: high in May-Sep (SW monsoon ~300mm/month); high again Oct-Dec (NE monsoon); dry Jan-Mar.

Reading patterns

  • Equatorial: consistently high T + heavy rain year-round (Singapore).
  • Tropical wet/dry: high T, distinct dry season (Yala SL summer).
  • Mediterranean: hot dry summer, mild wet winter.
  • Temperate: variable T, moderate rainfall.
  • Continental: wide T range, summer rain.
  • Tundra/Arctic: cold T, low precipitation.

7. Other Graph Types

Scatter Plot (சிதறிய புள்ளி வரைபு)

Two related variables as (x,y) points. Reveals correlation. Positive correlation: as X increases, Y increases (e.g., income vs life expectancy across countries). Negative: opposite.

Histogram (வரிசை வரைபு)

Bar-chart-like but shows frequency distribution. Continuous data binned into intervals. Y-axis = frequency. Used for: rainfall distribution, income distribution.

Choropleth Map (படிமப் பகுதி வரைபு)

Regional units shaded by data values. Darker = higher. e.g., population density per district map. SL versions widely used.

Cartogram

Distortion of map by data — country/district size proportional to a variable (population, GDP).

Pictograph

Categories represented by repeated icons proportional to value. e.g., one person icon = 1 million people.

8. Sample Exercises

அட்டவணை — SL agricultural export values.
அட்டவணை — SL agricultural export values. NIE பாடநூல், தரம் 11

Exercise 1: Best graph for SL population 1871-2012

Answer: Line graph — single line tracking time series; reveals J-curve growth.

Exercise 2: SL Ethnic composition 2012

Answer: Pie chart — categorical proportions sum to 100%; visualizes majority + minority.

Exercise 3: Compare SL districts by population

Answer: Bar chart (descending order) — easy comparison across discrete categories.

Exercise 4: SL imports vs exports 2010-2024

Answer: Multiple line graph (two lines) or grouped bar chart (one bar per metric per year).

Exercise 5: Climate of Anuradhapura

Answer: Climograph — temperature line + monthly rainfall bars on same x-axis.

Exercise 6: Tea exports 2010-2024 share by destination country

Answer: Pie chart for each year OR stacked area chart over time.

9. Common Mistakes + Best Practices

Common Mistakes

  • Wrong graph choice — pie chart for time-series; bar chart for proportions.
  • Missing axis labels + units — incomprehensible.
  • Inconsistent scale — distorts perception.
  • Too many categories in pie chart → unreadable.
  • 3D effects on bar/pie → distort perception.
  • Truncated Y-axis → exaggerates differences.
  • No title or source — graph orphaned.
  • Hard-to-read fonts/colors.
  • Pie slices not in size order.
  • Climograph: temperature on rainfall axis or vice versa.

Best Practices

  • Clear, descriptive title.
  • Label all axes with units.
  • Show data source.
  • Choose appropriate scale — avoid distortion.
  • Use color thoughtfully — avoid red/green confusion (color blind).
  • For pie: arrange slices by size + label percentages.
  • For line: include legend for multiple series.
  • Simplicity — fewer elements = clearer message.
  • Highlight key insight in title/annotation.
  • For maps: include scale + north arrow + legend.
⭐ பரீட்சைக் குறிப்புகள் — மறக்காதே
  • Choose graph for purpose: Trend = line; Compare = bar; Proportion = pie; Climate = climograph; Spatial = choropleth.
  • Line graph: time-series, continuous, X=time + Y=value.
  • Bar chart: compare categories. Simple/multiple/stacked/horizontal.
  • Pie chart: proportions sum to 100%. Calc angle = (value/total) × 360°. Max 7 categories.
  • Climograph: temperature line + rainfall bar; dual Y-axis.
  • Always include: title + axes labels (with units) + scale + source.
  • Avoid: 3D effects, truncated axes, too many categories, wrong graph choice.
  • Population pyramid: back-to-back horizontal bars for age-sex structure.
  • Scatter plot: for correlation between 2 variables.
  • Choropleth map: regional shading by data value.
⚠ மாணவர்கள் செய்யும் பொதுத் தவறுகள்
  • Pie chart for time-series — use line graph instead.
  • Bar chart for proportions — use pie chart instead.
  • Climograph: temperature on right axis, rainfall on left — convention is temp LEFT, rain RIGHT (but as long as labeled clearly, acceptable).
  • Pie angle calculation: (value/total) × 360° NOT 100°.
  • Truncated Y-axis exaggerates differences.
  • No legend for multiple series — viewer confused.
  • 3D effects in pie chart distort proportions.
  • Bar width inconsistent — looks unprofessional.
  • Climograph reading: temperature = line value (not bar height); rainfall = bar height.

✅ விரைவுச் சோதனை

முக்கியக் கருத்துக்களை உறுதிப்படுத்துங்கள். தவறான விடைகள் உங்கள் தவறுக் குறிப்பேட்டில் சேமிக்கப்படும்.

🖊 கட்டுரை வினாக்கள் (பகுதி II)

பரீட்சை வடிவில் கட்டமைப்பு வினாக்கள். முதலில் நீங்களே எழுதுங்கள்; பின்னர் மாதிரி விடையைத் திறந்து சரிபாருங்கள்.

1. \"Graph types + when to use them\" — பத்து graphs comparing strengths + uses. (8 புள்ளி)
2. \"Climograph + climate zones\" — construction + reading + zone identification. (8 புள்ளி)
3. \"Pie chart construction + interpretation\" — formula, examples, limits, best practices. (8 புள்ளி)

🔥 மீட்டல் மையம்

பரீட்சைக்கு முன் இறுதி ஒரு நிமிடம் — மறக்கக்கூடாதவை மட்டும்.

  • <b>Graph choice matrix:</b> Trend over time = Line; Compare categories = Bar; Proportion = Pie; Climate = Climograph; Correlation = Scatter; Spatial = Choropleth.
  • <b>Line graph:</b> X=time + Y=value. Best for continuous data trend.
  • <b>Bar chart:</b> compare categories. Simple/multiple/stacked/horizontal/100%.
  • <b>Pie chart:</b> proportional composition. Sum=100%. Angle = (value/total) × 360°. Max 7 categories.
  • <b>Climograph:</b> temperature line (left Y-axis) + rainfall bars (right Y-axis) × 12 months.
  • <b>Scatter plot:</b> correlation between 2 variables. Positive/negative/no.
  • <b>Histogram:</b> frequency distribution of continuous data binned.
  • <b>Choropleth map:</b> spatial data; regional shading by value.
  • <b>Cartogram:</b> map distorted by data (size proportional to variable).
  • <b>Pictograph:</b> repeated icons proportional to value.
  • <b>Population pyramid:</b> back-to-back horizontal bars (age-sex structure).
  • <b>Every graph must have:</b> title + axes labels with units + scale + source.
  • <b>Avoid:</b> 3D effects, truncated axes, wrong graph type, too many categories.

அலகின் முதுகெலும்பு — கருத்துக்களும் தொடர்புகளும்.

  • <b>Decision tree:</b> Time-series = line. Discrete category compare = bar. Proportion/composition = pie. Climate = climograph. Correlation 2 variables = scatter. Frequency distribution = histogram. Spatial = choropleth/cartogram. Demographic structure = population pyramid.
  • <b>Line graph detail:</b> X=independent (usually time). Y=dependent. Uniform scale both axes. Connect points smoothly. Multiple lines = legend. Compound = filled areas. Cumulative = running total.
  • <b>Bar chart detail:</b> Equal-width bars + equal gaps. Height = value. Best ordered by value descending. Variations: Simple (1 var per cat), Multiple (groups), Stacked (total + sub), 100% stacked (proportional composition), Horizontal (long names), Population pyramid (age-sex).
  • <b>Pie chart detail:</b> Calculate each angle = (value/total) × 360°. Draw circle. Mark angles from 12 o'clock clockwise. Largest slice first. Color/shade differently. Label name + % on each. Title + source. Verify sum = 360°.
  • <b>Pie angle examples:</b> 25%→90°; 50%→180°; 75%→270°; 100%→360°. Each 1% = 3.6°.
  • <b>Climograph detail:</b> X=12 months. Left Y=temp (°C). Right Y=rainfall (mm). Temperature plotted as line. Rainfall plotted as bars. Annual range = max-min temp. Annual total = sum monthly rainfall.
  • <b>Climate zone patterns:</b> Equatorial = stable hot + heavy rain year-round. Tropical wet-dry/savanna = hot + distinct wet/dry. Monsoon = bimodal rain. Mediterranean = mild winter wet + hot summer dry. Temperate = moderate variable. Continental = wide T range. Polar = cold + dry. Mountain = cool + variable.
  • <b>SL climographs:</b> Colombo wet zone (stable 27°C, dual rain peaks May-Sep + Oct-Dec, ~2400mm). Nuwara Eliya highland (13-16°C, SW monsoon peak May-Sep, 1900mm). Anuradhapura dry zone (24-31°C, Oct-Dec rain ~1300mm). Hambantota (26-30°C, Oct-Dec only ~1000mm).
  • <b>Scatter detail:</b> Each (x,y) point. Trend line optional. Reveals: Positive correlation (rise together); Negative (opposite); None; Outliers.
  • <b>Histogram detail:</b> Continuous data binned. Bars TOUCH (no gaps). Y=frequency. Shape reveals: Normal (bell), Skewed, Bimodal, Uniform.
  • <b>Choropleth detail:</b> Map of regions; each shaded by data value. Choose 4-7 color classes. Use sequential color (light to dark). Always include legend showing class ranges. e.g., SL population density by district.
  • <b>Cartogram detail:</b> Geographic distortion. Country/district size proportional to data (e.g., population, GDP). Reveals data magnitude vs geographic size.
  • <b>Pictograph detail:</b> Choose icon + unit value (1 icon = 1M people). Repeat icons proportionally. Good for general audience but imprecise.
  • <b>Population pyramid detail:</b> Horizontal back-to-back bars. Left = males; Right = females. Each row = age cohort. Shape reveals demographic stage: Broad-base = stage 2-3 (young growing); Rectangular = stage 4 (stable); Inverted = stage 5 (aging declining).
  • <b>Common errors:</b> Pie for time-series; Bar for proportions; Climograph axes reversed; 3D effects distort; Truncated Y-axis exaggerates; Wrong angle formula; Missing legend for multiple series; Too many pie categories; Missing source.

பரீட்சைக்கு முந்தின இரவு முழு அலகையும் ஓட்டிப் பார்.

  • <b>Memorize graph choice matrix:</b> Trend=Line; Categories=Bar; Proportion=Pie; Climate=Climograph; Correlation=Scatter; Distribution=Histogram; Spatial=Choropleth; Demography=Pyramid.
  • <b>Pie angle formula:</b> (value/total) × 360°. OR % × 3.6.
  • <b>Pie angle key values:</b> 25%=90°; 50%=180°; 75%=270°; 100%=360°.
  • <b>Must-have elements every graph:</b> Title + axes labels (with units) + scale + legend (if needed) + source.
  • <b>Climograph convention:</b> X=12 months; Left Y=Temp °C (line); Right Y=Rainfall mm (bars).
  • <b>SL climate zones (memorize):</b> Wet zone (Colombo 2400mm, Nuwara Eliya 1900mm), Dry zone (Anuradhapura 1300mm, Hambantota 1000mm), Intermediate.
  • <b>எளிதில் தவறும்:</b> (1) Pie chart NOT for time-series. (2) Bar chart NOT for proportions. (3) Climograph temperature is LINE not bar. (4) Pie angle = ×360 not ×100. (5) Truncated Y-axis misleads. (6) Don't use 3D effects.
  • <b>SL Geography applications:</b> Population growth (line); Districts compare (bar); Ethnic composition (pie); Climate (climograph); Income vs literacy (scatter); Density by district (choropleth); Age-sex (pyramid).
  • <b>கட்டுரைக்குத் தயார்:</b> (1) Graph types + when to use. (2) Climograph construction + reading + zones. (3) Pie chart construction + interpretation + best practices.
  • <b>Practical exam tasks:</b> (1) Given data → recommend graph type + reason. (2) Calculate pie angle for given percentage. (3) Construct climograph from monthly data. (4) Identify climate zone from given climograph. (5) Identify common errors in shown graph.
  • <b>Reading skills:</b> What is highest/lowest? Calculate range. Calculate total. Identify trend. Compare with another graph. Identify pattern type. Suggest interpretation.
  • <b>Best practices:</b> Simplicity + clarity + truthfulness > decoration. Choose right type for data. Include source. Use color thoughtfully. Avoid 3D + truncation + clutter.
📝 மேலும் பயிற்சி