about harmonic means

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Tahmid Hasan
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about harmonic means

Unread post by Tahmid Hasan » Tue May 24, 2011 12:27 pm

can harmonic mean be classified as one of the unique means because it is special form of AM. :?:
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Moon
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Re: about harmonic means

Unread post by Moon » Tue May 24, 2011 10:31 pm

Certainly it is a unique mean. Why do you think that this is a special form of AM? (Just because you are taking sum?)
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Re: about harmonic means

Unread post by Zzzz » Wed May 25, 2011 7:57 am

The first thing I found interesting about HM is - 'If you travel same distance at $a_1$ speed, then at $a_2$ speed,...,then at $a_n$ speed, your mean speed will be the HM of $a_1,a_2,...,a_n$. Not the AM. Also if the distance doesn't remain same, you can use weighted HM to find the mean speed.'
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Tahmid Hasan
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Re: about harmonic means

Unread post by Tahmid Hasan » Wed May 25, 2011 12:02 pm

i meant this
$\frac{\frac{1}{a_1}+......+ \frac{1}{a_n}}{n} \geq $ G.M.
conversing this expression gives me G.M. $\geq$ H.M.
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