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Am I the only one who sees a problem with yesterday's "average"?
Keiki Lemieux
I make HUDDLES
Join date: 8 Jul 2005
Posts: 1,490
05-09-2006 14:59
From: prak Curie
A better estimate of the price of a steak than $61.90.

It's not even right if you discard the outlier.
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Keiki Lemieux
I make HUDDLES
Join date: 8 Jul 2005
Posts: 1,490
05-09-2006 15:21
From: prak Curie
In some cases.
http://en.wikipedia.org/wiki/Harmonic_mean

You just proved my point with this one.

In this example, lets say the trip is 200 miles...

100 miles @ 40 mph
100 miles @ 60 mph

Let's try to solve this by multiplying miles by mph:

( 100 miles * 40mph + 100 miles * 60mph ) / ( 100 miles * 100 miles ) = 50mph

That isn't the right answer. The reason you get this wrong answer is because you are disregarding the units when multiplying distance * rate.

Instead, you should multiply miles * hours per mile like this:

( 100 miles * 0.025000 hours/mile + 100 miles * 0.016667 hours/mile ) / ( 100 + 100 ) = 0.02083 hours/mile

0.02083 hours/mile = 48 miles/hour

Notice also that the total time for this trip would be 4.1667 hours. And if you divide 200 miles by 4.1667 hours, you also get an average of 48 miles/hour. Harmonic mean is the same as what we commonly refer to as average, at least for rates.

In all of my examples you get the correct answer by multiplying so that the units cancel out:
  1. miles * hours/mile
  2. hours * miles/hour
  3. gallons * miles/gallon
  4. lindes * $/lindens
  5. $ * lindens/$


In Ricky's example the average is just like multiplying miles * mph, and that doesn't give you the harmonic mean. It gives you the wrong answer.
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Lawrence Linden
Linden Lab Developer
Join date: 25 Jun 2005
Posts: 235
05-10-2006 10:47
From: Elvawin Rainbow
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Lawrence Linden
Linden Lab Developer
Join date: 25 Jun 2005
Posts: 235
05-10-2006 10:55
I wish I'd seen this thread a few days ago, would have saved me some time. Great discussion here. For those who haven't seen it, I've updated the formula we use for average calculation. See this post for details.

Cheers,
Lawrence
Ricky Zamboni
Private citizen
Join date: 4 Jun 2004
Posts: 1,080
05-10-2006 11:08
From: Keiki Lemieux
In Ricky's example the average is just like multiplying miles * mph, and that doesn't give you the harmonic mean. It gives you the wrong answer.

*sigh* It doesn't give you the wrong answer. You just don't understand how probability distributions work. Now, having said that, I do agree that a harmonic mean is a valid way to calculate the average exchange rate.
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