What does an “average Australian” look like? After every census, this is one of those questions people like to see answered.
Average on one measurement or on many? If the latter, would the “average Australian” number in the millions, as most askers undoubtedly believe? Or will the “average” become unusual – a very small number, even a group that doesn’t actually exist?
What is the answer given by the Australian Bureau of Statistics? According to Teresa Dickinson, deputy national statistician at ABS, in 2021 “our average Australian” was “a woman aged 30 to 39 who lived in a coupled family with children, in a large capital region, with a weekly family income was. $3,000 or more”.
Let’s call this set of characteristics an identity – a bit like an artist’s sketch of a wanted person distributed to police officers as they go about the business of identifying “the person or persons of interest.”
In what sense is Dickinson’s identity valid, only useful?
One problem is that the characteristics he has chosen to highlight are not necessarily the characteristics that other people would choose. Dickinson framed his portrait along six dimensions: gender (controversially, the census largely omitted gender), age, relationship status, family structure (a measure that some Indigenous scholars have taken exception to), location and household income.
A very different picture could have been drawn around education, religion, ancestry, country of birth of parents, employment status, hours spent working unpaid, registered married status, housing structure, number of motor vehicles registered, etc. or was included. ,
Because Dickinson is addressing a question without context, the arbitrary nature of his choice is inevitable. The case involving less than six dimensions – or a distinct six – is neither weaker nor stronger than the case involving more than six.
Another problem is that the ABS treats the average categorical variables (gender, location, relationship status, family structure) as if they were continuous variables (such as age and income). If one person earns $30 per week, another $60, and a third $45, it makes sense to say that their average weekly income is $45. But if three people live in Brisbane, two in Perth and one in Wollongong, it makes no sense to say that on average six people live in Perth – or, really, anywhere.
Although she speaks of the average, Dickinson’s identity is actually based on mode (features that occur most frequently). This prompts him to include some groups while excluding others even when the difference is very small.
The most obvious and consequential example is the inclusion of women (50.7 percent of the population) and the exclusion of men (49.3%). Another example: the inclusion of women aged 30-39, but the exclusion of women aged 20-29, 40-49 and 50-59 may not exceed two percentage points, despite the difference in size in each of these groups. needed.
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Most shocking, however, is Dickinson’s failure to say whether his identity applies to a large number of Australians – the “typical” Australians of the popular imagination – or to only a small number.
Typically, identities cover a much smaller proportion of the population than – or are taken in by – might think. The greater the number of variables, the fewer individuals they represent. Given a sufficient number of variables – which is not necessarily a large number – the proportion of the population that represents an identity can be zero.
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In any identity, the least common characteristic among populations is the one that determines the upper bound of the number that can ever be included in the identity. In Dickinson, the least common feature appears to be women aged 30–39. According to the census, people in the age group of 30-39 were 14.5% of the population. So, women aged 30-39 are likely to have about 7%. If that’s the upper limit, it’s too low.
However, numbers that are identifiable can only be a fraction of it. From 7%, we need to subtract “couple families without children” (38.8 percent of all households) and those who do not live in the “greater capital area” (33.1 percent of the population). This could reduce the proportion that corresponds to identity to about 3 or 4% of the population, depending on the overlap between “coupled families without children” and those who do not live in “a large capital area”.
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If we now add up those with a median weekly family income of $3,000 or more – 24.3% of “occupied private residences” (though less, possibly, if any include the homeless, others) – the proportion of the population in which identikit is applied to some potential drops like 1%.
Maybe that also doesn’t do justice to the story. If Dickinson sought to identify the modal age within her 30-39 age range—a move that would have been entirely in line with the logic of her enterprise—the number of people matching her identity would suddenly disappear. A similar result would have occurred if it had chosen the modal income range among those with a median weekly household income of $3,000 or more.
Thanks to the census, we can say that in Australia there are: slightly more women than men; marginally higher in women aged 30-39 than in any other ten-year age group; And so on. We can’t say that the average Australian is: “A woman aged 30 to 39…” If it can’t be said, then the ABS shouldn’t even have thought to say it.