Graphical Representation and Mapping of Data

A table gives exact values in rows and columns, so it is the best form when precision matters. Its weakness is that trends are harder to spot than in a graph. In DI questions, a table is usually the data source, and the work is arithmetic on its cells. Always look for totals rows, units in the headnote (for example "in thousands") and footnotes.

A bar chart uses rectangular bars of equal width and equal gaps, and the length (or height) of a bar shows the value. It is suited to discrete or categorical data, such as sales by region or enrolment by state.

• Simple bar chart: one bar per category.

• Multiple (grouped) bar chart: bars for two or more series side by side, used to compare groups, for example boys and girls in each year.

• Sub-divided (stacked) bar chart: each bar is split into parts that add up to the whole.

• Percentage bar chart: every bar is scaled to 100 per cent, so it shows composition and not absolute size.

• Horizontal bar chart: used when category names are long.

Exam tip: in a stacked chart the top segment is read as the difference between the top and the lower edge, not from zero. Many students misread this.

A histogram is a set of adjacent rectangles with no gaps, drawn for a continuous frequency distribution. The class intervals are on the horizontal axis and frequencies on the vertical axis. The area of each rectangle is proportional to the frequency. If class widths are unequal, plot frequency density instead of frequency.

• Frequency polygon: made by joining the midpoints of the tops of the histogram bars with straight lines, and closing at both ends on the axis.

• Frequency curve: a smoothed polygon.

• Ogive (cumulative frequency curve): a "less than" ogive rises from left to right, and a "more than" ogive falls. The point where the two ogives cross gives the median. Plotting is done against the class boundaries.

A pie chart is a circle divided into sectors, each proportional to a part of the whole. It shows share or composition. It works well for 3 to 6 categories and poorly for many categories or for small differences.

\text{Angle of a sector} = \frac{\text{Value of the part}}{\text{Total}} \times 360^{\circ}

\text{Percentage share} = \frac{\text{Sector angle}}{360^{\circ}} \times 100

Useful angles: 1 per cent = 3.6°, 10 per cent = 36°, 25 per cent = 90°, 50 per cent = 180°, and 1° = 0.2778 per cent (about 5/18).

A line chart joins points with straight lines and is the standard choice for a time series. It shows rise, fall, fluctuation and the rate of change: a steeper line means a faster change, a flat line means no change. With several lines, the points where they cross mark times when the two values are equal. To find a percentage change between two years, read both values from the graph and use the percentage-change formula; do not judge it from the slope alone.

• Pictogram: uses symbols, with a key such as one symbol = 100 units.

• Scatter plot (scatter diagram): plots pairs of values to show the relationship between two variables. Points rising from left to right show positive correlation, falling points show negative correlation, and a cloud with no pattern shows no correlation.

• Area chart: a line chart with the area below filled, used for cumulative totals.

• Radar (spider) chart: compares several variables for one item on axes radiating from a centre.

• Box plot: shows median, quartiles and outliers.

• Stem-and-leaf plot: keeps the original values while showing the shape of the distribution.

• Bubble chart: a scatter plot where bubble size shows a third variable.

Mapping presents data by geographic location, which makes spatial patterns visible.

• Choropleth map: regions are shaded or coloured by a value, such as literacy rate by state.

• Dot map: each dot stands for a fixed count, such as 1 dot per 10,000 people.

• Proportional symbol map: the size of a symbol shows magnitude.

• Cartogram: the size of each region is distorted in proportion to the data value.

• Heat map: colour intensity shows density or concentration.

• GIS (Geographic Information System): software that captures, stores, analyses and displays spatial data in layers. It is used in disaster management, urban planning, agriculture, health surveillance and e-governance.

• Remote sensing: gathering data about the earth through satellites and sensors, often used with GIS.

Example 1. In a pie chart of a university's 3,600 students, the science sector has an angle of 120°. How many science students are there? Answer: (120 / 360) × 3,600 = 1,200.

Example 2. A pie chart shows household spending: food 30 per cent, rent 25 per cent, education 20 per cent, others 25 per cent. Find the angle for education. Answer: 20 per cent of 360° = 72°.

Example 3. Which graph best shows the monthly temperature of a city over a year? Answer: a line chart, because it is a time series.

Example 4. A histogram has classes 0 to 10, 10 to 20 and 20 to 40 with frequencies 5, 8 and 12. What should be plotted on the vertical axis for the last class? Answer: frequency density = 12 / 20 = 0.6, because its class width differs from the others.

Example 5. In a grouped bar chart, boys' enrolment is 40 and girls' is 50 in 2024. Girls are what per cent of total? Answer: 50 / 90 × 100 = 55.6 per cent.