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pari_alf

Member

Registered: 2013-12-01

Posts: 85

standard deviation formula

Hi guys,

I found a standard deviation formula from a paper.
The formula is shown as below,

I want you to please explain me formula a little in word.

Thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,167

Re: standard deviation formula

hi pari_alf

There are several steps needed to fully explain this.  I'll give an outline here; post back if you more details of any step.

(i) E(W) means the Expected value of W.  You can think of it as another way of writing this:

(ii)  The variance is defined this way:

Using the Expectation notation this would be

(iii) but it is possible to prove that this formula will also work

Back in the days before calculators this gave a quicker way of calculating the number.  Even with a calculator it has the advantage that the summations (there are three to do) can be done continuously as the data is entered, which, again, saves time.

In Expectation notation this is the formula you have discovered:

(iv) Then it's just a matter of taking the square root to get the standard deviation.

(v) I'm not sure why your formula starts with a function of x and y and then jumps into using W as the variable.  I have just used W throughout.  Perhaps W is a function of x and y ?

Hope that helps,

Bob

Last edited by Bob (2014-03-09 20:53:09)

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