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The geometric mean is better for quantities that are necessarily positive (like population), or that grow multiplicatively (like population).

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 10:04:55 AM EST
[ Parent ]
Maybe ... I'm more a picking the tool to fit the problem kind of economist, so I would say that in this case, that fact that the size of the other city in the pair is a main factor in determing the percentage market share leads one into the logarithmic family. Its a main reason why the ratio of populations between adjoining levels of the central place hierarchy tends to be close to constant (for most developed economies). And in the logarithmic family, the simplest mean is:

antilog( (log(x1)+log(x2))/2 )

which in direct arithmatic is:

(x1*x2)^.5

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Mon Mar 26th, 2007 at 11:03:05 AM EST
[ Parent ]
Exactly.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Mon Mar 26th, 2007 at 05:34:49 PM EST
[ Parent ]

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