I think your problem is the initial assignment to $num. Your code is confused: that C<for> statement is not a loop, its just an assignment. But the assignment should be inside the month loop, because you are calculating the average per month. A clearer coding of this might be:

  foreach my $month (@calendar)
  {
    my $count = 0;
    my $total = 0;

    foreach my $value (
         grep { $_ != 0 }
         map { $hoursWorked{$_}{$month} }
         @members )
    {
       $total += $value;
       $count ++;
    }

    $avg{$month} = $count ? $total/$count : 0;
  }
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--Dave