Statistical Graphs, Charts and Maps in Geography
Senior 5 · Geography
Statistical Graphs, Charts and Maps in Geography
Lesson 3 of 4
25 min
The two drawings in Figure 7 are age–sex pyramids. They describe two invented countries, A and B, but their shapes are those of real countries. Before reading any number, look at the outline. Country A has a very wide base that narrows quickly, like a tall triangle: many children, few old people. Country B is narrow at the base, widest in middle age, and thick at the top. The shape alone tells a geographer a great deal about births, deaths, life expectancy and future needs.
Definition
Age–sex pyramid (population pyramid): a pair of horizontal bar graphs drawn back to back, males on the left and females on the right, one bar for each age group (usually 5 years), youngest at the bottom. Bar length is the number, or the percentage of the total population, in that age group and sex. Example: Figure 7.
| Shape | Example in Figure 7 | What it shows |
|---|---|---|
| Expansive (progressive): wide base, concave sides, narrow top | Country A | High birth rate, high death rate at all ages, short life expectancy, rapid growth; a young population |
| Constrictive (regressive): base narrower than the middle | Country B | Falling birth rate, low death rate, long life expectancy; slow growth or decline; an ageing population |
| Stationary: nearly straight sides until old age | (not shown) | Low birth and death rates that have balanced for a long time; little growth |
Look for details as well as the outline. In Country B the top bar (75+) is longer for females (4.4%) than for males (2.7%), because women usually live longer than men. A bar that is suddenly short in the middle of a pyramid can record a past event: a war, an epidemic, or the emigration of young adults to work abroad.
Definition
Dependency ratio: the number of dependants (people aged 0–14 and 65 and over) for every 100 people of working age (15–64).
Example: if 40% are under 15, 5% are 65 or over and 55% are 15–64, the ratio is .
Worked example 1: dependency ratios from Figure 7
Problem. In Country A the groups 0–14 make up 42.9% of the population and the groups 65+ make up 2.3%. In Country B the figures are 14.5% and 17.8%. Calculate both dependency ratios and compare them.
Solution. Working-age share: A: ; B: .
Country A has about 83 dependants per 100 workers, almost all of them children; it must spend heavily on schools, vaccination and food. Country B has about 48, and more of them are old than young: it needs pensions, health care for the elderly and, eventually, workers from elsewhere.
Definition
Divided circle (pie chart): a circle divided into sectors whose angles are proportional to the parts of a whole. A sector's angle is . Example: Figure 8, each province's share of Rwanda's population.
A divided circle answers the question "what share?" rather than "how many?". Figure 8 shows at once that the Eastern Province holds the largest share of Rwanda's people (26.9%) and Kigali City the smallest (13.2%). The bar under the circle shows the same five shares as a divided bar: one bar, 100% long, split into segments. A divided bar is easier to draw with a ruler, and several of them (one per year) can be stacked to show how shares change over time.
Worked example 2: calculating sector angles
Problem. In 2022 Kigali City had 1,745,555 people out of Rwanda's 13,246,394. Find the sector angle.
Solution.
Do the same for each province: Eastern 96.8°, Southern 81.6°, Western 78.7°, Northern 55.4°. Their sum is 359.9°, not 360°, because each was rounded. Make the largest sector absorb the difference (draw Eastern as 96.9°) so that the circle closes. Start at the 12 o'clock line and draw the sectors clockwise, largest first, with a protractor.
A single pie shows shares but not size. To compare totals as well, draw a proportional circle for each total, with its area proportional to the value. Because the area of a circle is , the radius must be proportional to the square root of the value. These circles can then be divided like pie charts, giving proportional divided circles, which are often placed on a map, one per district or country.
Worked example 3: the radius of a proportional circle
Problem. The circle for Rwanda's 2012 population (10.52 million) has a radius of 2.0 cm. Find the radius for 2022 (13.25 million).
Solution.
The population grew by 26%, but the radius grows by only 12%. If you made the radius 26% larger, the area would grow by and exaggerate the growth.
| Method | Advantages | Disadvantages |
|---|---|---|
| Age–sex pyramid | Shows age and sex structure together; its shape reveals birth and death trends and past events | Needs detailed census data; percentages and numbers are easily confused; hard to compare more than two |
| Divided circle | Shows parts of a whole clearly; attractive and easy to understand | Angles are hard to compare by eye; small sectors (under about 5°) are hard to draw and label; needs a calculation for every sector |
| Divided bar | Easy to draw; several can be compared side by side | Only the first segment starts at a common base, so the others are hard to compare |
| Proportional circle | Shows both size and composition; can be placed on a map | Square roots are needed; the eye underestimates differences in area |
Warning
Common mistakes
Tip
Exam technique. To describe a pyramid, work from the bottom up in four steps: the base (birth rate), the sides (death rate and life expectancy), the top (proportion of elderly) and any notches or bulges (past events or migration). Quote at least two figures read from the graph.
Mr. Sinn: "Understanding Population Pyramids & The DTM". Watch how each pyramid shape is linked to birth rates, death rates and a stage of growth, then compare his shapes with Countries A and B in Figure 7.
Practice
Summary
Sources and credits
Written by Ganzaa. Figure 7 uses illustrative data invented for teaching. Figures 8 and 9 use the 2012 and 2022 census totals of the National Institute of Statistics of Rwanda (NISR), statistics.gov.rw; the angles, percentages and radii were calculated by Ganzaa. All figures were drawn by Ganzaa.
Video: "Understanding Population Pyramids & The DTM (AP Human Geography)", Mr. Sinn, embedded from YouTube.
