What’s wrong with this picture?

I only read two web pages daily: theage.com.au and /. (The rest I either skim via RSS or only stumble across occasionally)

Normally relegated to the Herald Sun, the logic flaws in this article this morning astound me:

The bureau estimates that Melbourne’s population grew by 74,713 in the year to last June and, on revised figures, by 74,791 the year before that.

Hmmm ok, so that’s a fair few bodies. How’s that fit the bigger picture?

Bureau of Statistics figures show the city is on track to have 4 million people by the end of this year, after its population growth increased to an annual rate of 2 per cent.

OK, some context. 2%. Sounds like a lot.

Melbourne’s population growth last year far outpaced all other major Australian cities.

Hmmm… being the 2nd biggest city in the country, and a cheaper one than the largest, this isn’t that surprising. Still, good to know. I wonder how we compare quantitatively…

Sydney’s population grew by 55,047 or 1.3 per cent, Brisbane by 43,404 (2.3 per cent) and Perth by 43,381 (2.8 per cent).

Hmmm… maybe they mean more net peeps = good mkay? Out-pacing? Doesn’t look like it on population growth… maybe they mean something else…:

The label of Australia’s fastest-growing city might once have been one for which Melbourne yearned…

Sorry boys. Still is! Of the four cities listed, Melbourne has the 2nd slowest rate of growth. In order to “outpace” something, you need to move faster over time with respect to the thing being measured. Population Growth rate (i.e. expressed as a percentage) is a measure of acceleration, not displacement! (Wiki article)

If this were a physics problem, you’d be working with the following data:

Starting Point
Melbourne: 3,900,000 people
Sydney: 4,400,000 people
Brisbane: 1,950,000 people
Perth: 1,600,000 people

t = t + 1
After one year (unit of time), you’d have:
Melbourne: 3,900,000 + 74,791 = 3,974,791 people
Sydney: 4,400,000 + 55,047 = 4,455,047 people
Brisbane: 1,950,000 + 43,404 = 1,993,404 people
Perth: 1,600,000 + 43,381 = 1,643,381 people

Calculate Velocity:
The velocity of each of these movements is: (trivial, as the unit and quantum of time is the same in each above)
Melbourne: 74,791/year
Sydney: 55,047/year
Brisbane: 43,404/year
Perth: 43,381/year
Of these, Melbourne certainly has the greatest velocity (net displacement over time). It might be the fastest moving (if all were on the same starting line and you are measuring only net increase in numbers).

Calculate Acceleration:
However, it is not the fastest growing: (from the article):
Melbourne: 2%
Sydney: 1.3%
Brisbane: 2.3%
Perth: 2.8%

Conclusion:
At present rates, Melbourne will never catch up to Sydney, and Perth will eventually catch up to Melbourne (in approx 115 years).

Moving on to the rest of the article:

In a national perspective, it was the year of the west. Perth added almost as many people as Brisbane, growing by 43,381 people or 2.8 per cent. And south-western Western Australia grew more quickly than either the Sunshine Coast or the Gold Coast, its population rising by almost 9000 or 3.9 per cent.

Cairns had the fastest growth rate of the big regional cities, 4.1 per cent, but has since gone into a deep recession with the loss of Asian tourists.

Ha! Now we find that not only did Melbourne’s growth not even outpace Sydney or Brisbane, but it’s failed to keep up with three separate parts of Queensland as well! Seriously, the entire contention of this article is absolutely bogus!

The most surprising thing here is not that journalists have zero understanding of basic mathematical concepts. No, the most surprising thing is they then get the concept of pace/rate of growth right in the second page of the same article! (i.e. the Cairns quote above). So we’ve got a situation where Cairns with a 4.1% rate of growth has been “outpaced” by Melbourne’s 2% rate of growth. Someone had better teach me more quantum mechanics fast – I’m trying to reconcile two parallel universes here!

Of course, it’s possible they mean that the rate of growth of Melbourne’s rate of growth is out-pacing other cities, but that’s neither in the data nor the argument presented in the article.

Reminds me of Bob Cringely’s excellent post on the bailout of the US banks, back when he was writing for PBS.

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