ABS Demographic data comparing the age distributions of Indigenous and non Indigenous Australians is analysed and interpreted using summary statistics and parallel box plots. Note the data is presented in a grouped frequency table and so cumulative frequency using the midpoint is used to estimate centre and spread.
Access to CAS calculators or Excel
Copy of student worksheet
Optional: Computer with Internet connection
Comparing the Age Distributions of Indigenous and Non-Indigenous Australians
Every 5 years the Census collects population data and in intervening years estimated resident populations (ERP) are produced. In non-Census years 'non-Indigenous' population counts are created by subtracting Indigenous population estimates or projections from total ERP.
The following population pyramids show the projected age distributions of all Australians and Indigenous Australians for 2013 (Midway between the 2011 and 2016 Censuses). They can be found on the Australian Bureau of Statistics web site.
In this activity you will compare and report on the age distributions of Indigenous and Non-Indigenous Australians using various statistical measures and graphical displays.
The following data tables relate to the age distribution for NSW. Data for other states and territories can be found in the source documents shown beneath each table and could also be used to complete this activity. Note that these data use Indigenous population projections.
Task One: Calculating Summary Statistics
Because of the amount of raw data available for population by age, it is presented in tables using 5 year intervals. One disadvantage of using data that is arranged in class intervals is that it is not possible to calculate exact measures such as mean, median and mode. Instead an estimate can be made using a mid-point to represent the data in each interval.
E.g. for the age interval 0 – 4, (0, 1, 2, 3, 4) the mid-point is 2.
To make it easier to calculate and draw graphs you can copy and paste the date into an Excel or other spread sheet application. Show all calculations correct to the nearest year.
1. Measures of Centre
Using a spread sheet fill in the mid-point and cumulative frequency columns.
Step 1: Finding the estimate of the mean
The mean is found by =
Step 2: Finding the estimate of the median
The position of the median is located by where n is the number of data.
Calculate the value of and using the cumulative frequency column, locate the interval that contains this value. Use the mid-point of this interval to fill in the estimate of the median below.
Step 3: Finding the estimate of the mode
The mode is the most frequently occurring interval. Use the mid-point of this interval to fill in the estimate of the mode.
NSW age distribution
Mode (excluding 75+)
2. Measures of Spread
NSW age distribution
Range ( max – min)
IQR (Q3 – Q1)
Task Two: Displaying the Data
3. Using the data in Figures 3 and 4 draw a separate histogram for each group and comment on each.
4. Based on the same method used to find the median, find Q1 and Q3. Use a 5 figure summary to draw parallel box and whisker plots for each group. Comment on each.
5. Below are box plots from the Indigenous and non-Indigenous populations Australia for the year 1991. Comment on how the age distributions have changed since then.
Using ABS data for a different State or Territory repeat the investigation and compare your results with those for NSW.
Unless otherwise noted, content on this website is licensed under a Creative Commons Attribution 2.5 Australia Licence together with any terms, conditions and exclusions as set out in the website Copyright notice. For permission to do anything beyond the scope of this licence and copyright terms contact us.