How to calculate the median weekly personal income?

How to
Median-income
Georgia Allan

Georgia Allan

Customer Success Manager

Key Highlights:

  • The Australian Census provides personal income data in ranges rather than exact figures. This article outlines a method to estimate the median weekly personal income using this grouped data.
  • Step-by-Step Calculation Process:
    • Export the relevant income data into Excel.
    • Exclude the “Not stated” category to ensure accuracy.
    • Recalculate the total number of persons aged 15 and over.
    • Determine the percentage distribution across income ranges.
    • Compute cumulative percentages to identify the income range containing the 50% mark.
    • Apply interpolation within this range to estimate the median income.
  • Using data from the City of West Torrens, the article demonstrates that the median falls within the $400–$599 income bracket. Through interpolation, the median weekly personal income is estimated at approximately $546.
  • This methodology is valuable for local councils and planners aiming to derive median income figures from publicly available census data, facilitating informed decision-making in community planning and resource allocation.

How to calculate the median weekly personal income?

Something we get asked for a lot here at .id is median weekly personal income.

While it’s not available on our profile.id sites, you can calculate it from the ranged personal income data on the site.

You can find the data here (I’m using the City of West Torrens for this example, my old stomping ground!):

Export the data from the Weekly individual income table into Excel

Once Excel opens, this is what it should look like

The next step is to remove the “Not stated” category, and recalculate the percentages (I’ve also deleted the Greater Adelaide column, so we don’t all get confused) Firstly, recalculate the Total persons aged 15+

Then calculate the new percentages (putting the ‘$’ between the B and the 15 means it will always divide by this cell, even as you drag the formula down)

The next step is to calculate the cumulative percentages as you progress through the income ranges

The formula for the first cell is a bit different, but from the second one you can just drag the same formula down

The next step is to determine in which income range the 50% mark falls. As you can see from the example, the median for West Torrens falls somewhere within the $400-$599 range

Next you need to work out the difference between this range and the one below it

Then calculate the difference between 50% and the same lower income range

Now divide this new value by the one calculated a few steps ago. This value shows how far into the identified income range the median falls

So in the case of West Torrens we can see that the median falls 0.73 of the way through the $400-$599 income range. To work out what that is, multiply the dollar amount in the range (in this case $200) by the proportion you just calculated

Add this amount to the lower amount of the income range (in this case $400)

Now you have your median income!

To access demographic information for communities across Australia, please visit our demographic resource centre.

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