Re: Standard Deviation

Hello,

Why is this squaring required?

Sum of the squares of the deviation from mean gives the power of the
current sample deviation and when we add all these powers up, and divide by
total number of samples, we get the variance, root of which gives standard
deviation, in other words, we're taking the root of the average deviation "power" of
the signal to get the deviation or fluctuation of the signal from the mean value,

How is this different from "adding all the (sample value - mean) values
and dividing by the total number of samples?

When you add all the (observation - mean) values, the results equals 0.
And 0 divided by N still equals 0.

You could add all the absolute values of the (observation - mean)
values, but, in doing so, you are implicitely giving the same weight
to, for instance, 1 large deviation of 10 points and to 10 little
deviations of 1 point.

Thus, in your analysis, you probably want to assign a larger weight to
1 big error than to 10 littles errors. One (amongst others) way to do
so is to square all the (observation - mean) values, so that 10
deviations of 1 point will have a "weight" of 1 each, and 1 large
deviation of 10 points will have a "weight" of 100 in calculating the
deviation.

I hope this was clear enough.

Fabrice.

.

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