about harmonic means
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
can harmonic mean be classified as one of the unique means because it is special form of AM.
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Re: about harmonic means
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
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
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: about harmonic means
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.
$\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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