Chapter 3 Graphical Representation Of Data

Presenting data in organised formats like tables helps make it understandable (as learned in the previous chapter). However, visual representations such as graphs, diagrams, and maps significantly enhance comprehension, facilitate comparisons, save time, and offer a simplified view of complex information.

Consider how thematic maps showing population distribution, climate, or resource distribution provide an immediate visual impression that would be difficult to obtain from just tables or descriptive text.

General Rules For Drawing Graphs, Diagrams And Maps

To effectively represent data visually, certain general rules and principles should be followed:

Selection Of A Suitable Method

Different types of data and the characteristics they represent require different graphical methods for optimal representation. The choice of method should be appropriate for the theme of the data.

• Data showing trends over time (time series data), such as changes in temperature, rainfall over months, or population growth over years, are best represented by Line Graphs.
• Data for comparing values across different categories or geographical units, such as total rainfall in different cities or the production of various commodities, are often represented by Bar Diagrams.
• To show the distribution of phenomena across space, like population, livestock, or crop areas within administrative units, Thematic Maps (like dot maps or choropleth maps) are used.

Selection Of Suitable Scale

Choosing an appropriate scale is crucial for accurately representing data on diagrams and maps. The scale translates the numerical values of the data into visual measurements (like length of bars or size of symbols).

The selected scale must accommodate the entire range of data values to be represented, from the minimum to the maximum. The scale should be neither too large (making the diagram/map too big or unable to fit all data) nor too small (making the diagram/map cramped and difficult to read).

Design

The overall design elements are important for creating a clear and informative visual representation. Key components of good cartographic design (applicable to diagrams and maps) include:

• Title: Clearly states what the diagram or map represents, including the geographical area covered, the specific subject matter, and the year or period the data refers to. The title, often with a subtitle and year, is usually placed centrally at the top. Different font sizes and thickness can be used for hierarchy.
• Legend (Index): Explains the meaning of all colours, shades, patterns, symbols, and signs used within the diagram or map. A well-drawn legend ensures the reader can correctly interpret the visual elements. It should be clearly positioned, typically at the bottom left or right of the visual.
• Direction: For maps (representing geographical space), indicating direction, usually North, is essential for orientation. A North arrow symbol should be drawn and properly placed on the map.

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Construction Of Diagrams

Diagrams visually represent data characteristics like length, width, and volume. They can be categorized based on the dimensions used for representation:

• One-dimensional diagrams: Use primarily length to represent values (e.g., line graph, bar diagram).
• Two-dimensional diagrams: Use area to represent values (e.g., pie diagram, rectangular diagram).
• Three-dimensional diagrams: Use volume to represent values (e.g., cube diagram, spherical diagram).

We will focus on the construction of commonly used diagrams.

Line Graph

Line graphs are primarily used to represent time series data, showing how a variable changes over a continuous period (months, years). They are suitable for depicting trends in data like temperature, rainfall, population growth rates, birth rates, or death rates over time.

Construction Steps:

• Round off data values to simplify plotting, if necessary.
• Draw two perpendicular axes: the horizontal X-axis and the vertical Y-axis. The time period variable (years, months) is marked on the X-axis, and the quantitative values of the data (e.g., population growth %, temperature °C) are marked on the Y-axis.
• Select an appropriate scale for the Y-axis and label it. Ensure the scale covers the entire range of data values, including negative values if present.
• Plot each data point by finding the intersection of the corresponding point on the X-axis (time period) and the selected value on the Y-axis. Mark each plotted point clearly, usually with a dot.
• Join the plotted points with straight lines to form the line graph.

Answer:

Polygraph

A polygraph is a type of line graph used to compare the trends of two or more variables over the same period. It uses multiple lines within a single graph to represent the different variables.

To distinguish between the lines representing different variables, different line patterns (solid, broken, dotted, combination) or different colours can be used.

Answer:

Bar Diagram

Bar diagrams use columns of equal width to visually represent data. They are also known as columnar diagrams and are effective for comparing values across different categories or over time.

Rules for Construction:

• All bars must have the same width.
• Bars should be separated by equal intervals or distances.
• Bars can be shaded or coloured distinctly for clarity and visual appeal.

Based on data characteristics, bar diagrams can be simple, multiple, or compound.

Simple Bar Diagram

A simple bar diagram represents a single variable across different categories for direct comparison. For non-time series data, arranging categories in ascending or descending order of values can improve clarity. For time series data, bars are plotted according to the sequence of time periods.

Answer:

Line And Bar Graph

Sometimes, a line graph and a bar diagram can be combined into a single diagram to represent two closely related variables, especially when one represents a trend (like temperature) and the other represents discrete values (like rainfall) over the same time period (e.g., months). Climate data is a common example.

In a combined graph, months are typically on the X-axis, while the two variables (temperature and rainfall) are plotted on separate Y-axes on either side of the graph using their respective scales.

Answer:

Multiple Bar Diagram

Multiple bar diagrams are used to compare the values of two or more related variables across different categories or time periods. Each category or time period is represented by a group of bars, with each bar in the group representing a different variable.

Answer:

Compound Bar Diagram

A compound bar diagram (or stacked bar diagram) represents the different components that make up a total value within a single bar. The total length of each bar represents the total value, and this bar is divided into segments (rectangles) corresponding to the proportions or values of its components.

Answer:

Pie Diagram

A pie diagram (or divided circle diagram) is a circular statistical graphic used to represent proportions or percentages of a whole. The entire circle represents the total value (100%), and the circle is divided into sectors (slices of the pie) where the area of each sector is proportional to the quantity or percentage it represents.

The angle of each sector is calculated based on its value relative to the total. If values are given as percentages, the angle for each percentage is calculated as:

$ \text{Angle for Category } x = \frac{\text{Percentage of } x}{100} \times 360^\circ $

If data is given in absolute values, the angle is calculated as:

$ \text{Angle for Category } x = \frac{\text{Value of } x}{\text{Total Value}} \times 360^\circ $

Answer:

Precautions: The circle size should be appropriate. Measuring angles starting with smaller values can help in accurate plotting. Use distinct shades/colours and include all design elements (title, legend).

Flow Maps/Chart

A flow map (or flow chart or dynamic map) visually represents the movement or 'flow' of commodities, people, or traffic between origins and destinations. It uses lines of proportional width on a map to show the quantity of movement along specific routes.

Flow maps can represent data like the number and frequency of vehicles, or the quantity of goods or passengers transported.

Requirements:

• A base map showing the routes and connecting points (stations, cities).
• Data on the quantity of flow (goods, passengers, vehicles) along each route segment and the points of origin/destination.
• A scale to relate the quantity of flow to the width of the lines drawn on the map.

Answer:

Answer:

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Thematic Maps

While diagrams are useful for comparisons, thematic maps are specifically designed to show the geographical distribution patterns or variations of a particular theme or characteristic over space. These are also known as distribution maps.

Requirements:

• Relevant data for the selected theme at the level of administrative units (state, district, etc.).
• An outline map of the study area with administrative boundaries.
• Sometimes, a physical map (e.g., physiographic map for population distribution, relief/drainage map for transport) is needed to accurately place features or interpret distribution.

Rules for Making Thematic Maps:

• Planning is essential for clarity. The final map must include:
  • Name of the area covered.
  • Title describing the subject matter.
  • Source and year of data.
  • Legend explaining symbols, signs, colours, or shades used.
  • Scale of the map.
• Selecting a suitable mapping method is crucial based on the nature of the data (quantitative or qualitative).

Classification based on Method:

• Quantitative Maps: Show variations in numerical data across administrative units or space (e.g., population density, rainfall categories). Also called statistical maps.
• Non-quantitative Maps: Depict qualitative differences or presence/absence of features without showing specific numerical variations (e.g., areas of high/low rainfall). Also called qualitative maps.

We will focus on the construction methods for the following types of quantitative thematic maps:

• Dot maps
• Choropleth maps
• Isopleth maps

Dot Maps

Dot maps use dots of a uniform size, placed within administrative units, to show the distribution of a phenomenon where each dot represents a chosen quantity. The density of dots reflects the density of the phenomenon.

Requirements:

• Administrative map with boundaries.
• Statistical data for the phenomenon for each administrative unit (e.g., total population, cattle count).
• A chosen scale determining the value represented by each dot.
• A physical map to help place dots accurately within the administrative unit, reflecting actual distribution (e.g., avoiding placing dots in water bodies, mountainous areas, or deserts if representing population).

Precautions:

• Administrative boundaries should not be overly prominent.
• All dots must be of the same size to maintain visual consistency.
• Dot placement should ideally reflect the actual distribution within the unit, guided by physical geography.

Answer:

Choropleth Map

Choropleth maps represent statistical data (like density, rates, percentages) related to administrative units by using different shades, patterns, or colours to indicate different classes or categories of data values within each unit.

Requirements:

• Map showing administrative units.
• Statistical data for each administrative unit.

Steps for Construction:

• Arrange the data values for all administrative units in ascending or descending order.
• Group the data into a suitable number of categories (classes), typically 5, representing different ranges (e.g., very low, low, medium, high, very high).
• The interval for each category can be calculated by dividing the total range of the data (Maximum value - Minimum value) by the number of categories.
• Assign different shades, patterns, or colours to each category. The intensity of the shading or colour should increase or decrease with the value range of the categories (e.g., lighter shades for lower values, darker shades for higher values).
• Apply the assigned shades/patterns/colours to the corresponding administrative units on the map based on their data value category.
• Include all necessary map design elements (title, legend, source, scale, etc.).

Answer:

Isopleth Map

Isopleth maps are used to represent continuous data (like temperature, pressure, rainfall, elevation) where values vary smoothly across space, not abruptly between administrative units. These maps use lines called isopleths, which connect points of equal value.

The word 'Isopleth' comes from 'Iso' (equal) and 'pleth' (lines). Examples include Isotherms (equal temperature), Isobars (equal pressure), Isohyets (equal rainfall), Contours (equal height), etc.

Requirements:

• Base map with the locations of observation points (where data was collected).
• Data values for the phenomenon at each observation point for a specific period.
• Drawing instruments, particularly a French Curve, for drawing smooth lines.

Rules for Drawing:

• Select a consistent interval between isopleth values (e.g., every 5°C, every 10 mm). Intervals of 5, 10, or 20 are often considered ideal.
• Label the value of each isopleth line, either along the line or in the middle by breaking the line.
• Lines should be drawn smoothly.

Interpolation: This is the process of estimating intermediate values between known data points and locating the exact position where an isopleth line of a specific value should pass between two observation points.

Method of Interpolation:

• Find the minimum and maximum data values on the map. Calculate the range.
• Determine the interval for the isopleths based on the range.
• To locate the exact point for an isopleth between two points with known values, measure the distance between the points on the map. Calculate the difference between the values at the two points. Determine how far the desired isopleth value is from one of the known values.
• The position of the isopleth between the two points can be estimated using the formula:

  $ \text{Distance from Point 1} = \frac{\text{Difference between Value at Point 1 and desired Isopleth Value}}{\text{Difference between Value at Point 1 and Value at Point 2}} \times \text{Distance between Point 1 and Point 2} $

  For example, if points A (28°C) and B (33°C) are 10 mm apart, and you want to plot the 30°C isotherm: Difference between A and B is 5°C. 30°C is 2°C away from A (28°C). Distance from A = $(2/5) \times 10 \text{ mm} = 4 \text{ mm}$. So, the 30°C line passes 4 mm from point A (and 6 mm from point B).

• Draw the isopleths, starting with the minimum value line, and subsequent lines at the chosen interval. Draw them smoothly using a French curve.

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Excercises

This section contains exercises designed to test understanding of graphical and thematic map representation techniques, including identifying suitable methods, interpreting diagrams/maps, and steps for construction.