
2 Attachment(s)
Help with summation
Note: I accidentally posted this in the precalculus subforum. 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)
Attachment 27292
Where x_{m} 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 :)

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.

Re: Help with summation
On another note, why is this NOT precalculus? I thought sums and sequences were precalculus?

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!

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.)