# Help with summation

• Feb 28th 2013, 04:13 AM
spearo
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)

Attachment 27290

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.
• Feb 28th 2013, 01:25 PM
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 $\displaystyle M x_m$ and the bottom to $\displaystyle x_m$, where M and $\displaystyle x_m$ are constants.
$\displaystyle \frac{\sum\limits_{m=1}^{12} M_m.x_m}{\sum\limits_{m=1}^{12}x_m}$
then this can be interpreted as a weighted average over the months of the year, letting $\displaystyle M_m$ be a variable dependent on m running from 1 (January) to 12 (December)
Expanding we would get $\displaystyle \frac{1x_1 + 2x_2 + ... + 12x_{12}}{x_1 + x_2 + ... + x_{12}}$