Tcl, 118115 bytes
proc S L {lmap c $L {expr ($c-[set m ([join $L +])/[set n [llength $L]].])/sqrt(([lmap c([join $L {list +-$m)**2+($c]-$m)**2}])/$n)}}
Tcl, 126118 bytes
proc S L {lmap c $L {expr ($c-[set m ([join $L +])/[set n [llength $L]].])/sqrt(([join [lmap c $L {exprlist +($c-$m)**2}] +])/$n)}}
Tcl, 129126 bytes
proc S {L q\ 0} {lmap c $L {set qexpr ($q+($c-[set m ([join $L +])/[set n [llength $L]].])**2)}
lmap/sqrt(([join [lmap c $L {expr ($c-$m)/sqrt($q**2}] +])/$n)}}