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  SELECT department, count(department)
  FROM table
  GROUP BY department

use strict;

...
                         }
                         keys %testhash;
print( "$musicstudents\n" );

   my %outputhash = somefunction(\%testhash, 'department');

  # my %outputhash = ( music => 3,
  #                    chemistry => 2 );

  my %outputhash;
  $outputhash{$_->{department}}++ for grep { $_->{department}
                                            } values %testhash;