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Math Help - Help with summation

  1. #1
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    Help with summation

    Hello all,

    I would like to ask what is probably a simple question for you all... *blush*

    I am having some trouble understanding the notation of an equation used to calculate the timing of the seasonal peak of plankton.

    Here it is: (I am afraid I am unfamiliar with TeX, so I will simply paste an image of the equation...)

    (Central Tendency, T)

    Help with summation-t.jpg

    Where xm is the mean abundance in month M (January=1, Feb=2,...,Dec=12)

    I understand that the denominator is simply SUM from 1 to 12 the mean abundance i.e. X1 + X2... +X12. I don't understand the M.xm part, though; does the full stop/period/dot represent a multiplication...?

    Apologies if this is all elementary...

    Many thanks in advance for any help offered

    I have realised this is in the incorrect sub-forum and have reposted it in the algebra sub-forum. Apologies.
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    Last edited by spearo; February 28th 2013 at 05:06 AM. Reason: wrong sub-forum
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Help with summation

    The summation you posted actually makes no sense. Since the terms in the sums are dependent on m and not i then the sum on the top evaluates to M x_m and the bottom to x_m, where M and x_m are constants.

    If instead the expression is
    \frac{\sum\limits_{m=1}^{12} M_m.x_m}{\sum\limits_{m=1}^{12}x_m}

    then this can be interpreted as a weighted average over the months of the year, letting M_m be a variable dependent on m running from 1 (January) to 12 (December)

    Expanding we would get \frac{1x_1 + 2x_2 + ... + 12x_{12}}{x_1 + x_2 + ... + x_{12}}
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  3. #3
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    Re: Help with summation

    Many thanks!
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