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Math Help - Help with summation

  1. #1
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    Help with summation

    Note: I accidentally posted this in the precalculus sub-forum. Please accept my apologies for cross posting. If a mod could remove the other thread I would be grateful. Once again, sorry for poor etiquette...
    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
    Attached Files Attached Files
    • File Type: pdf T.pdf (66.7 KB, 6 views)
    Last edited by spearo; February 28th 2013 at 06:02 AM. Reason: fix attachment
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  2. #2
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    Re: Help with summation

    Hey spearo.

    Basically what is going on is that the denominator acts as a kind of normalizing constant which turns the frequencies (the x's) into probabilities.

    Once this is done, your formula is just the formula for the mean of a distribution and this is exactly what the central tendency is.

    Without the normalizing constant on the denominator, you would have probabilities and the expression wouldn't give the right measure.
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  3. #3
    Senior Member Paze's Avatar
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    Re: Help with summation

    On another note, why is this NOT pre-calculus? I thought sums and sequences were pre-calculus?
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  4. #4
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    Re: Help with summation

    Many thanks!

    Paze, I guess it is, but after reading the stickies, I was worried it may have not have been. I thought as my question was more regarding the notation I would ask in general algebra. Apologies for my hapless forum etiquette!
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  5. #5
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    Re: Help with summation

    One more little addition to that. In some instances "." means something very particular in the context of a sum. The sum from i = 1 to n of x_i., for instance, would mean that there is some other set of numbers j that are part of the sum, but aren't being summed inside the summation operation. This means you are only summing against i rather than some other index. (This is a tricky thing to explain. But if you are having more trouble with it and can't get numbers to work that might be the thing! Hope that's helpful.)
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