Overall nice code minus the comments - but there have been enough comments about the comments so I refrain from commenting on that :)

I'd restructure the loop for reading in the input file a bit:

use List::Util qw/sum/;

while( <INPUT> )
{
  next if /^$/;
  my ($first, $last, @grades) = split;

  my $name_index = "$last,$first";
  my $avg_grade = sum(@grades) / scalar(@grades);

  $students{$name_index}{grades}    = \@grades;
  $students{$name_index}{avg_grade} = $avg_grade;

  push @averages, $avg_grade;
}
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As you can see, I split the line directly into the needed parts. Furthermore the variable only needed in this loop are declared inside the loop - this locality gives less chances for mistakes.

I don't know whether you are allowed to use modules to solve your exercise - but the sum subroutine from List::Util comes in handy here. Otherwise you could just program the sub yourself. I don't see any point in rounding the results you push into @averages. You are only using this internally and why not calculate with the whole precision you have available - thus simplifying the code. You could still do the rounding when you print something out.

A final remark to a differnt part of the code, this: my $i = sprintf("%d", scalar(@averages) / 2 ); could be better written as my $i = int( scalar(@averages)/2 ); Both do rounding towards zero.

-- Hofmator