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
<div class="wimscenter">
Standard deviation =
!htmlmath $res2
<br />
Standard deviation of sampling =
!htmlmath $res1
</div>
Data: $cnt numbers { $formula }
<p>
The <em>standard deviation</em> (resp. <em>standard deviation of
sampling</em>) of 
\(\{x_1, x_2, ..., x_n\}\) 
is equal to
!set ins_align=middle
!insmath \sqrt{{1\over n}\sum_{i=1}^n (x_i-\overline{x})^2}
 (resp.
!insmath \sqrt{{1\over n-1}\sum_{i=1}^n (x_i-\overline{x})^2}
&nbsp;), where
!set ins_align=bottom
!insmath \overline{x}
 is the <em>arithmetic mean</em> of the data.
</p>
!exit