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CTK Exchange
iliaden
Member since Aug-14-05
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Apr-04-06, 06:21 PM (EST) |
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"statistics"
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I have recently bumped into an physics problem. when I was solving it, I was unable to find the correct terminology for the following "mean" 1st number: 9/(0.11-0.01)=90 2nd number: 9/(0.11+0.1)=75 Since I was calculating the spread because I had to calculate 9/(0.11+-0.1). After doing this, I wanted to find the "mean" (let's call it like that for now) by doing the following: 9/0.11=81.8181818... I know that the arithmetic mean would be (90+75)/2=82.5 What is the name of that "mean" I found? please help! |
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mr_homm
Member since May-22-05
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Apr-04-06, 08:42 PM (EST) |
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1. "RE: statistics"
In response to message #0
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Hi iliaden, I have heard this called the reciprocal mean or inverse mean. What you have done is the same as taking the numbers A and B, and computing 1/C = (1/A + 1/B)/2, in other words, the reciprocal of the mean of the reciprocals. This kind of reciprocal mean sometimes shows up in computing things in physics like gravitational ro electrical potential energy, where the value depends on 1/radius. --Stuart Anderson
>1st number: 9/(0.11-0.01)=90
>2nd number: 9/(0.11+0.1)=75
>
>9/0.11=81.8181818...
>
>I know that the arithmetic mean would be (90+75)/2=82.5
>What is the name of that "mean" I found?
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iliaden
Member since Aug-14-05
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Apr-07-06, 10:36 AM (EST) |
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3. "RE: statistics"
In response to message #2
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Thanx a lot for the answers, but I thought that the harmonic mean was evaluated as follows: arithmetic mean/geometric mean=geometric mean/harmonic mean, or geometric mean^2/arithmetic mean=harmonic mean
Ilia Denotkine
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mr_homm
Member since May-22-05
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Apr-07-06, 12:24 PM (EST) |
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4. "RE: statistics"
In response to message #3
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Hi Ilia, >geometric mean^2/arithmetic mean=harmonic mean This is also true! (geometric mean)^2 = ab arithmetic mean = (a+b)/2 1/(harmonic mean) = (1/a+1/b)/2
Now try them out in your formula:
ab/((a+b)/2) = 2ab/(a+b) 1/((1/a + 1/b)/2) = 2/(1/a + a/b) = 2/((b+a)/ab) = 2ab/(a+b) So you see they are the same. This also shows a fun property of these three means: Let
gm = geometric mean, am = arithmetic mean, hm = harmonic mean,
and let
A = am(a,b), B = hm(a,b).
Then the gm has the nice property that gm(a,b) = gm(A,B), i.e. the gm of the hm and am is the same as the gm of the original two numbers.
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