standard deviation of an arbitrary number of numbers using bc or other standard utilities

Using awk:

standardDeviation=$(
    echo "$myNumbers" |
        awk '{sum+=$1; sumsq+=$1*$1}END{print sqrt(sumsq/NR - (sum/NR)**2)}'
)
echo $standardDeviation

Using perl :

#!/usr/bin/env perl

use strict; use warnings;
use Math::NumberCruncher;

my @data = qw/
    0.556
    1.456
    45.111
    7.812
    5.001
/;

print Math::NumberCruncher::StandardDeviation(\@data);

Output

16.7631

Population standard deviation:

jq -s '(add/length)as$a|map(pow(.-$a;2))|add/length|sqrt'
ruby -e'a=readlines.map(&:to_f);puts (a.map{|x|(x-a.reduce(:+)/a.length)**2}.reduce(:+)/a.length)**0.5'
jq -s '(map(.*.)|add/length)-pow(add/length;2)|sqrt'
awk '{x+=$0;y+=$0^2}END{print sqrt(y/NR-(x/NR)^2)}'

In awk, ^ is in POSIX but ** is not. ** is supported by gawk and nawk but not by mawk.

Sample standard deviation (the first two commands are the same as the first two commands above, but length was replaced with length-1):

jq -s '(add/length)as$a|map(pow(.-$a;2))|add/(length-1)|sqrt'
ruby -e'a=readlines.map(&:to_f);puts (a.map{|x|(x-a.reduce(:+)/a.length)**2}.reduce(:+)/(a.length-1))**0.5'
R -q -e 'sd(scan("stdin"))'

Or use GNU Octave (which can much more than simple std):

standardDeviation="$(echo "${myNumbers}" | octave --eval 'disp(std(scanf("%f")))')"
echo $standardDeviation

Outputs

18.742