This article is republished from The Conversation under a Creative Commons license. Read the original article here.

What does “the average Australian” look like? After every census, this is one of the questions people like to see answered.

Average on one measure or on several? If the latter, would “average Australians” number in the millions, as most inquirers no doubt assume? Or would the “average” turn out to be atypical – a very small number, even a group that doesn’t actually exist?

What is the answer offered by the Australian Bureau of Statistics? According to Teresa Dickinson, deputy national statistician at the ABS, “our average Australian” in 2021 was “a female aged 30 to 39 years, living in a coupled family with children, in a greater capital city area, with a weekly family income of $3,000 or more”.

Let’s call this set of characteristics an identikit – a bit like the artist’s sketch of the wanted person distributed to police officers as they go about the business of identifying the “person or persons of interest”.

An average of what?

In what sense is Dickinson’s identikit valid, let alone useful?

One problem is that the features she has chosen to highlight are not necessarily the features others would choose. Dickinson builds her portrait along six dimensions: sex (controversially, the census largely steered clear of gender), age, relationship status, family composition (a measure to which some Indigenous scholars have taken exception), location and household income.

A very different portrait could have been built around – or included – education, religion, ancestry, parents’ country of birth, employment status, hours spent doing unpaid work, registered married status, dwelling structure, number of registered motor vehicles, and so on.

Because Dickinson is addressing a question without context, the arbitrary nature of her choices is inevitable. The case for including fewer than six dimensions – or a different six – is neither weaker nor stronger than the case for including more than six.

Choices: the ABS average doesn’t include religion.
Lukas Coch/AAP

Conflating the average and the mode?

Another problem is that the ABS average treats categorical variables (sex, location, relationship status, family composition) as if they were continuous variables (like age and income). If one individual earns $30 a week, another $60, and a third $45, it makes sense to say that their average weekly income is $45. But if three individuals live in Brisbane, two in Perth and one in Wollongong, it makes no sense to say that on average the six live in Perth – or, indeed, anywhere.

Although she talks of averages, Dickinson’s identikit is actually based on modes (the most frequently occurring charateristics). This leads her to include some groups while excluding others, even when the differences are very small.

The inclusion of women (50.7% of the population) and the exclusion of men (49.3%) is the most obvious and consequential example. Another example: the inclusion of women aged 30–39 but the exclusion of women aged 20–29, 40–49 and 50–59 despite the differences in the size of each of these cohorts probably being no more than two percentage points.

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Diminishing returns

What is most striking, however, is Dickinson’s failure to say whether her identikit applies to a large number of Australians – the “typical” Australian of popular imagination – or to only a small number.

Typically, identikits cover a much smaller proportion of the population than those who create them – or are taken in by them – might think. The greater the number of variables, the fewer the number of individuals they represent. Given a sufficient number of variables – which needn’t be a large number – the proportion of the population that an identikit represents can drop to zero.

In any identikit, the least common characteristic among the population is what sets the upper limit on the number the identikit could ever encompass. In Dickinson’s, the least common characteristic appears to be women aged 30–39. According to the census, people aged 30–39 made up 14.5% of the population. So, women aged 30–39 are likely to have constituted around 7%. If that’s the upper limit, it’s pretty low.

Yet the numbers that fit the identikit can only be a fraction of this. From the 7%, we need to subtract “coupled families without children” (38.8% of all families) and people who don’t live in “a greater capital city area” (33.1% of the population). This could reduce the proportion that fits the identikit to around 3 or 4% of the population, depending on the overlap between “coupled families without children” and people who don’t live in “a greater capital city area”.

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If we now add those with an average weekly family income of $3,000 or more – 24.3% of those in “occupied private dwellings” (though fewer, presumably, if one includes the homeless, among others) – the proportion of the population to which the identikit applies very likely drops to something like 1%.

Even that may not do the story justice. Had Dickinson sought to identify the modal age within her 30–39 age range – a move that would have been entirely consistent with the logic of her enterprise – the number of people that matched her identikit might suddenly have become vanishingly small. A similar result would have emerged if she had chosen the modal income range among those with an average weekly family income of $3,000 or more.

Thanks to the census, we can say that in Australia: there are slightly more women than men; marginally more women aged 30–39 than in any other ten-year age group; and so on. What we can’t say is that the average Australian is: “A female aged 30 to 39 years…” If it can’t be said, the ABS shouldn’t even be thinking of saying it.

This article is republished from The Conversation under a Creative Commons license. Read the original article here.