sub sum {
    reduce { $a + $b } 0, @_; 
}
sub avg {     
    return undef unless @_; # avoid division by 0
    sum (@_)/scalar @_;
}
sub variance {
    return undef unless @_; # avoid division by 0
    my $avg = avg (@_);
    sum ( map {($_ - $avg)**2} @_ )/ scalar @_;
}
sub std_dev {   
    sqrt variance (@_);
}