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geometric mean q

by oops » Fri Jun 08, 2007 12:48 pm
Question in one of the online test resource says arithmetic mean is always greater than geometric mean unless the two no.s are equal.
They give the proof that (a+b)/2 = Root (a.b) iff a=b
Seems correct.

However, after looking up the defn of geometric mean at wolfram mathworld, it seems to me that above may not be true - i.,e if two no.s are negative, geometric mean is +ve, whereas arith mean is -ve.

Is it the case that geometric mean is not defined for -ve no.s ?
If you have a definitive answer or insight, please clarify.
(Posted on gmatclub with no response so far)

Thanks.
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Re: geometric mean q

by gabriel » Sat Jun 09, 2007 8:27 am
oops wrote:Question in one of the online test resource says arithmetic mean is always greater than geometric mean unless the two no.s are equal.
They give the proof that (a+b)/2 = Root (a.b) iff a=b
Seems correct.

However, after looking up the defn of geometric mean at wolfram mathworld, it seems to me that above may not be true - i.,e if two no.s are negative, geometric mean is +ve, whereas arith mean is -ve.

Is it the case that geometric mean is not defined for -ve no.s ?
If you have a definitive answer or insight, please clarify.
(Posted on gmatclub with no response so far)

Thanks.
geometric mean is very much defined for -ve numbers ...

the rule that ur referring to is actually that.. the arithmetic mean is greater than or equal to the geometric mean .. in which the numbers considered are positive ... that is this rules is applicable only when the nembers are greater than 0 ( positive) ...

... for eg. consider a set of positive numbers a,b,c,d,e ... upto "n" numbers

the rule is defined as .... (a+b+c+d+e+...)/n >= (a*b*c*d*e*..)^1/n .. hope this helps ..
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Re: geometric mean q

by oops » Sat Jun 09, 2007 2:26 pm
gabriel wrote:
oops wrote:Question in one of the online test resource says arithmetic mean is always greater than geometric mean unless the two no.s are equal.
They give the proof that (a+b)/2 = Root (a.b) iff a=b
Seems correct.

However, after looking up the defn of geometric mean at wolfram mathworld, it seems to me that above may not be true - i.,e if two no.s are negative, geometric mean is +ve, whereas arith mean is -ve.

Is it the case that geometric mean is not defined for -ve no.s ?
If you have a definitive answer or insight, please clarify.
(Posted on gmatclub with no response so far)

Thanks.
geometric mean is very much defined for -ve numbers ...

the rule that ur referring to is actually that.. the arithmetic mean is greater than or equal to the geometric mean .. in which the numbers considered are positive ... that is this rules is applicable only when the nembers are greater than 0 ( positive) ...

... for eg. consider a set of positive numbers a,b,c,d,e ... upto "n" numbers

the rule is defined as .... (a+b+c+d+e+...)/n >= (a*b*c*d*e*..)^1/n .. hope this helps ..

thanks for the response.
however, the question doesn't state that the no.s are positive, integers, or any such thing - hence the confusion.
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