Statistical and Graphical Methods

What you need to know

• A simple bar graph compares the totals of separate items with bars of equal width whose lengths are proportional to the values. Bars are drawn apart, not touching, and must start from zero or the comparison is dishonest. Use it when you want a quick comparison of a few items, such as cocoa output in six states.
• A group or compound bar graph places the bars for each sub-item side by side within each category, so you compare components across categories, for example maize, rice and sorghum output in 2020, 2021 and 2022.
• A divided or component bar graph stacks the components on top of each other within one bar whose total length is the total for that category. Use it when both the total and the breakdown matter. Shade each component differently and provide a key.
• A pie chart or divided circle shows how a single total is shared out. Each value is converted to degrees by dividing it by the total and multiplying by 360, and the sectors are drawn clockwise from twelve o'clock, usually largest first. A pie chart is unsuitable for more than about six or seven components because thin slices cannot be read.
• A divided rectangle does the same job as a pie chart using a rectangle of convenient length, usually 10 cm. Each component is converted into a length by dividing the value by the total and multiplying by the chosen length. It is easier to draw accurately than a pie chart and easier to compare across years.
• A line graph or simple line chart shows change over time, so it is the correct choice for temperature through the year, population from 1960 to 2020 or crude oil output month by month. Time always goes on the horizontal axis and the quantity on the vertical axis.
• A climatic graph combines a bar graph of monthly rainfall with a line graph of monthly temperature on a shared time axis with two vertical scales, rainfall on one side and temperature on the other. It is the standard way of presenting the climate of a station.
• Proportional circles represent values at different places by circles of different sizes, where the radius is proportional to the square root of the value, not to the value itself, because area grows as the square of the radius. Placing them on a base map shows both quantity and location.
• A dot map shows distribution by placing dots of fixed value over the map, so each dot stands for a stated number of people, animals or tonnes. It shows pattern and density well but exact totals must be counted, and dots cannot be crowded beyond readability.
• A choropleth or shading map divides the area into administrative units and shades each according to the class its value falls into, darker shading for higher values. It must be used for rates, ratios and densities, never for absolute totals, because a large state would otherwise look important simply for being large.
• An isopleth or isoline map joins points of equal value with lines, giving isotherms for temperature, isohyets for rainfall, isobars for pressure and contours for height. It suits data that change gradually and continuously across space.
• A flow line or flow map shows movement between places, with the width of each line drawn proportional to the volume moved, for example traffic on roads out of Lagos or the export of cocoa from producing states to the ports.
• Match the method to the data before you pick up the pencil. Comparison of separate totals takes a bar graph; a share of one whole takes a pie chart or divided rectangle; change over time takes a line graph; a rate or density across areas takes a choropleth; quantity at specific points takes proportional circles; movement takes flow lines.
• Every diagram must carry a title that states what, where and when; a stated scale or vertical axis scale; labelled axes with units; and a key where shading or colour is used. Marks are awarded for these separately from the accuracy of the drawing, so a correctly drawn diagram without a key still loses marks.