Cumulative standard deviation

Using a closure:

sub sd (@a) {
    my $mean = @a R/ [+] @a;
    sqrt @a R/ [+] map (* - $mean)², @a;
}
 
sub sdaccum {
    my @a;
    return { push @a, $^x; sd @a; };
}
 
my &f = sdaccum;
say f $_ for 2, 4, 4, 4, 5, 5, 7, 9;

Using a state variable (remember that <(x-<x>)²> = <x²> - <x>²):

sub stddev($x) {
    sqrt
        ( .[2] += $x²) / ++.[0]
      - ((.[1] += $x ) /   .[0])²
    given state @;
}

say .&stddev for <2 4 4 4 5 5 7 9>;

Output:

0
1
0.942809041582063
0.866025403784439
0.979795897113271
1
1.39970842444753
2