References auto-vivify in Perl; if you have a variable with an undefined value, and you treat it as a reference, Perl creates the reference for you. Thus, the push should be sufficient for all cases:
push @{ $statistics{$line_number} }, $thisline;
Although, if you want to be more explicit, you can create the array ref yourself:
$statistics{$line_number} ||= [];
push @{ $statistics{$line_number} }, $thisline;
There's also an example of this in
perlreftut (offsite), the tutorial on references.
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