Interpreting population pyramids and choropleth maps

For ages 60 and over, A has $9+10=19\%$, whereas B has $13+15=28\%$. B has a greater proportion in this older group. These comparisons explain the shapes: A is wider at the bottom, while B has relatively wider bars at older ages.

To compare a broader range, add all the relevant bars. For example, the proportion aged 40 and over in A is $12+11+9+10=42\%$. In B it is $14+14+13+15=56\%$. This supports the conclusion that B has a greater proportion aged 40 and over; it does not establish why their age distributions differ.

Comparing the two sides also reveals differences within a population. In B's 60-and-over group, females account for 15% of the whole population and males account for 13%. Because these percentages use the same denominator, there are more females than males in that age group.

Proportions are not population totals

Percentage pyramids make it easier to compare the age structures of differently sized populations, but they do not show which population has more people unless totals are also supplied.

For example, suppose A contains 10,000 people and B contains 20,000 people. Using their percentages aged 0–19, A has $0.30\times10\,000=3000$ people in that group, while B has $0.20\times20\,000=4000$. A has the greater proportion, but B has the greater number.

In general:

The relevant total must match the percentage basis. A percentage of females must be applied to the female population total, not automatically to the whole population.

If percentages have been rounded, converting them into counts gives estimates rather than exact counts. Several different counts can produce the same rounded percentage. Rounding can also make displayed percentages total slightly more or less than 100%.

Reading a choropleth map

A choropleth map represents data for different regions using colours, shades or patterns. Each region is filled according to the interval containing its value. The regions might be geographical areas, or subdivisions of a space such as a field.

Start with the title to identify the variable and time represented. Then read the key, including its units and interval boundaries. Darker shading often indicates higher values, but the key—not the appearance alone—establishes this. On a black-and-white diagram, different patterns may be used instead of colours.

For example, if a key has intervals $0\leq p<20$ and $20\leq p<40$, a value of 20 belongs in the second interval. Non-overlapping intervals ensure that each value has exactly one shading category.

Comparing spatial patterns

These maps show the percentage of residents who cycle regularly in six fictional regions at two times. They use identical boundaries and an identical key. They are not maps of a real place or measured observations.

At time 1, regions A and D are in the lowest interval, below 20%. At time 2, A has moved into the 20% to below 40% interval, while D remains below 20%. Region A's percentage has therefore increased enough to cross an interval boundary.

Region E also moves upwards, from 20% to below 40% into 40% to below 60%. At time 2, C, E and F form a group of higher-valued regions on the right of the diagram. This describes a spatial pattern without assuming its cause.

Region F has the same shade at both times. This means its value remains in the same interval—not necessarily that its percentage is unchanged. Likewise, C and F share a shade, but their exact percentages need not be equal.

On other maps, compare the keys before comparing shades. If the boundaries or intervals change, an apparent change in shading may not represent a change in the underlying value. Also distinguish the mapped variable from region size: a physically larger shaded region does not necessarily have a higher percentage or contain more people.

The same reading method transfers to authentic maps: identify the variable, read the key, locate regions, describe patterns and support comparisons with intervals. A choropleth map groups values, so it usually reveals ranges and spatial patterns rather than exact values or explanations for those patterns.

Rounded percentages produce estimated counts.

Choropleth maps

• Read the title, time, units and shading key.
• Identify high and low intervals, clusters and differences between regions.
• Compare maps using their keys and region boundaries, not shades alone.
• Same shade means same interval, not necessarily the same value.
• Region area does not represent the mapped percentage.
• Describe the pattern; the map alone does not establish its cause.

Read each choropleth key: the same shade can represent different intervals on different maps.

The way people or observations are spread across different ages or age groups.