






This classroom activity compares the size of Australia’s state capitals and develops the use of proportional symbols to represent the data. There are two opportunities for extension. For a more accurate representation of the data, proportional circles may be drawn by making calculations of the areas of a circle. A second option for extension involves the integration of the statistics into a geographic information system (GIS) in order to develop the skills of digital thematic mapping.





 Map of Australia showing states and territories
 Tracing paper
 Computer and GIS software






1. Represent the area of each capital city as a proportional circle drawn accurately to scale. The instructions for calculating proportional circles are shown below.
When proportional circles are used, the area of the circle represents the population of the city. To draw a circle the radius must first be calculated. This is done by obtaining the square root of each capital city population and choosing an appropriate scale to represent the data.
Population of city (P) is to be represented by the area of a circle = Πr^{2 }. Therefore the radius is proportional to the square root of the population.
When all radii have been calculated choose a suitable scale to represent the data. On an Australian map (A4) size, then a scale for each radius could be 1mm represents 100 people.
Example: Brisbane
Population = 1,810,900 and radius is represented by √1,810,900 = 1345.70 If 1 mm is used to represent a radius of 100 then Brisbane would be represented by a circle with radius of 13.5mm.
This activity could be delivered with the aid of a geographic information system. The thematic mapping capability could be used to accurately draw the proportional symbols



TABLE 2. POPULATION OF AUSTRALIA'S CAPITAL CITIES, JUNE 2006

Capital city  (a) Rank (101508) according to the size of population.  (b) Estimate the population of Australian capital cities.  Population capital city statistical division, June 2006 
Adelaide    1 146 119 
Brisbane    1 820 400 
Canberra    333 940 
Darwin    114 368 
Greater Hobart    205 566 
Melbourne    3 744 373 
Perth    1 519 510 
Sydney    4 284 379 
Source: Table 7.19, Year Book Australia, 2008 (cat # 1301)
TABLE 3. CALCULATIONS FOR CREATION OF PROPORTIONAL SYMBOLS TO REPRESENT THE POPULATION OF AUSTRALIA'S CAPITAL CITIES 
Capital city  Population capital city statistical division, June 2006  Square root of population  Possible scale for A4 map (1mm represents 100 people) 
Adelaide  1 146 119  1070.57  10.7 
Brisbane  1 820 400  1349.22  13.5 
Canberra  333 940  577.88  5.8 
Darwin  114 368  338.18  3.4 
Greater Hobart  205 566  453.39.  4.5 
Melbourne  3 744 373  1935.04  19.4 
Perth  1 519 510  1232.68  12.3 
Sydney  4 284 379  2069.87  20.7 



Estimated Resident Population (ERP)
Is the count of all people regardless of citizenship and nationality, who usually live in Australia, with the exception of foreign diplomats and their families. It is the official measure of the Australian population.
Proportional symbols
Symbols used on a map where the size of the symbol is proportional to the value it represents.



Note: Links to ABS publications are to the most recent release. Previous releases can be accessed by selecting the Past and Future Releases tab.
Year Book Australia, 2008 (cat no 1301.0)


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