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what does Harmonic mean means ?

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what does Harmonic mean means ? [#permalink] New post 22 Oct 2009, 19:18
if X, Y and Z are in Harmonic Progression, what is the Harmonic mean of this series ?

what does Harmonic mean means ?
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Re: what does Harmonic mean means ? [#permalink] New post 22 Oct 2009, 19:22
reciprocal of AP ..

a , a /1+d , a/1+2d........
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Re: what does Harmonic mean means ? [#permalink] New post 22 Oct 2009, 19:28
sorry, could not get you .........I asked Harmonic mean
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Re: what does Harmonic mean means ? [#permalink] New post 22 Oct 2009, 19:33
Let me give one examples say ...

if i have 3,4,6 as harmonic series..what is the harmonic mean ?


do i do it like sum of all terms / number of terms = (3+4+6)/3 =13/3

Or

do I reciprocate the things first to convert it into a AP
i.e 1/3,1/4,1/6 are now in AP .....Now again I am stuck here because We are asked to find Harmonic mean , So do i calculate the Arithmetic mean i.e (1/3+1/6)/2or just mean by the formula sum of all terms / number of terms i.e (1/3+1/4+1/6)/3 ?


So, As you see I have messed up now ....whats the right direction ? I need explanation why I should choose one path and why to discard the other ?
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Re: what does Harmonic mean means ? [#permalink] New post 18 Oct 2012, 07:32
In my opinion, Harmonic mean = N Divided by (summation of individual reciprocals of N terms).
For example, harmonic mean of 1,2,3 will be

3 / [(1/1) + (1/2) + (1/3)]
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Re: what does Harmonic mean means ? [#permalink] New post 18 Oct 2012, 10:14
ghentu wrote:
if X, Y and Z are in Harmonic Progression, what is the Harmonic mean of this series ?

what does Harmonic mean means ?


For two numbers "x" and "y" the arithmetic mean = \frac{x+y}{2}

Harmonic mean = (\frac{1}{x} + \frac{1}{y}/2)^-1

i.e Raised to the power of -1
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Re: what does Harmonic mean means ?   [#permalink] 18 Oct 2012, 10:14
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