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Topic: Standard deviation
Replies: 2   Last Post: Jan 28, 2013 9:50 AM

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 Jos Posts: 1,268 Registered: 10/24/08
Re: Standard deviation
Posted: Jan 28, 2013 9:42 AM

"Paul " <paulrockt@gmx.de> wrote in message <ke61o4\$4n8\$1@newscl01ah.mathworks.com>...
> Hi together,
> i calculate the standard deviaton in MATLAB and to the check the results i reculculated manually in MATLAB and Excel and i got different results. I split the formula in MATLAB to calculate the individual terms and as result i have received the same as in Excel. Is there a known problem with the standard deviation in MATLAB?
>
> My example:
>
> test = -18.2264 -17.7185 -15.4258 -15.4092
>
> mean_test = -16.6950 <<< mean_test= mean(test)
>
> sqr = 278.7222 <<< sqr= mean_test^2
>
> test_sqr = 332.2018 313.9459 237.9556 237.4423 <<< test_sqr= test.^2
>
> diff = 53.4796 35.2237 -40.7666 -41.2799 <<< diff = bsxfun(@minus,test_sqr,sqr)
>
> sum = 6.6568 <<< summe = sum(diff(:))
>
> norm = 1.6642 <<< norm = 0.25*summe
>
> final = 1.2900 <<< final = norm^0.5
>
> my results
>
> in Excel: 1.2901
> in MATLAB (manually): 1.2900
> in MATLAB (with "stdev"): 1.0931
>
> Can someone explain this to me?
>
> Thanks,Paul

From the help of STD
" STD normalizes Y by (N-1), where N is the sample size. This is the
sqrt of an unbiased estimator of the variance of the population from
which X is drawn, as long as X consists of independent, identically
distributed samples.

Y = STD(X,1) normalizes by N and produces the square root of the second
moment of the sample about its mean.
"
Indeed, for your example, std(test,1) gives 1.29 ...

doc std
and
http://en.wikipedia.org/wiki/Standard_deviation

hth
~ Jos

Date Subject Author
1/28/13 Jos
1/28/13 Torsten