Subversion Repositories wimsdev

!goto $wims_read_parm

:def
title=Standard deviation
synonyme=deviation, normal deviation, data deviation, mean square deviation
input=data1d
!exit

:proc

cnt=!itemcnt $formula
!if $cnt<2
 !exit
!endif

sum=!sum x for x in $formula
mean=$[($sum)/$cnt]
fm=!sum (x-($mean))^2 for x in $formula
res1=$[sqrt($fm/($cnt-1))]
res2=$[sqrt($fm/$cnt)]
result=$res1\
$res2

!exit

:output
<center>
Standard deviation =
!htmlmath $res2
<br>
Standard deviation of sampling =
!htmlmath $res1
</center> <p>
Data: $cnt numbers { $formula }
<p>
The <em>standard deviation</em> (resp. <em>standard deviation of
sampling</em>)
of {<i>x</i><sub>1</sub>,
<i>x</i><sub>2</sub>, ..., <i>x<sub>n</sub></i>} is equal to
!set ins_align=middle
!instex $$$$ \sqrt{{1\over n}\sum_{i=1}^n (x_i-\overline x)^2} $$$$
 (resp.
!instex $$$$ \sqrt{{1\over n-1}\sum_{i=1}^n (x_i-\overline x)^2} $$$$
&nbsp;), where
!set ins_align=bottom
!instex $$ \overline x $$
 is the <em>arithmetic mean</em> of the data.

!exit