use List::Util qw(min max sum);

my $min = min keys %hash;
my $max = max keys %hash;
my $avg = sum(keys %hash) / keys %hash;

# Won't work: avg keys %hash;
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Untested, btw. I'm not sure what you mean with shortest and longest numerical key. I'll assume here you mean minimum and maximum. If you mean shortest string-wise, use minstr and maxstr instead.

Update: Doh! There is no avg function. Code is updated to reflect that.

[ ar0n ]