Re: Taking a blithe dare

[William Cala <Wcala@ROCHESTER.RR.COM>]

Ah yes..... exhibit A in support (?) of mathematics as a graduation
requirement.
And I thought "hamonic mean" had something to do with a well-balanced nasty
guy.

BC

----- Original Message -----
From: "Art Burke" <aburke@VANSD.ORG>
To: <ARN-L@listsrva.CUA.EDU>
Sent: Tuesday, February 12, 2002 11:32 AM
Subject: Re: Taking a blithe dare


Nope. The harmonic mean is weighted by the number of cases.

For N numbers (none zero), the harmonic mean is N/(1/x1 + 1/x2 + ... +
1/xN).  For the two-point case, as in the posted problem, the harmonic mean
is (2*x1*x2)/(x1+x2).  The harmonic mean of (2 and 3, the data from the
posted problem) is 2*3*2 / 5 = 2.4.

Art


>>> Victor.Steinbok@VERIZON.NET 02/12 8:13 AM >>>
At 7:08 AM -0800 2/12/02, Art Burke wrote:
>Nope, it's the reciprocal of the sum of the reciprocals.  Art

Yes, Art. That's what a harmonic mean is.

        VS-)


>  >>> Victor.Steinbok@VERIZON.NET 02/11 9:29 PM >>>
>At 2:04 PM -0800 2/11/02, Art Burke wrote:
>>The solution for two painters is T = A*B / A+B.
>>
>>The solution in the case of N painters is T = 1/ (1/A + 1/B + 1/C + ...
1/N),
>>     where A, B, C ... N are the times the different painters take to
>>paint the room.
>
>Of course, the two comments you made are equivalent for two painters.
>All are harmonic means.
>
>         VS-)

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