... i can't figure out how to clear the foreach loop for every new set of data it uploads from a file.

The push built-in only adds elements to the end of an array (as you have discovered). Somewhere near the top of the main
    while (1) { ... }
loop and before reading the file into the array, add a
    @array = ();
statement to clear the array.

Better yet, IMHO: Because the  @array array is not used outside the while-loop in this code, only declare the array at the point at which it is needed. (The same applies to the  $average scalar.) Something like

my @array;

while (my $data = <FH>) {
    push @array, $data;
}
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or more simply, forget the while-loop and just

my @array = <FH>;
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Combined with the change to the  average() function that pryrt suggested, things should go more smoothly.

Update: Note that in the

foreach (@array) {
    chomp;
    if ($average > $_) {
    print "$_\t is below average.\n";
    } elsif ($average < $_) {
        print "$_\t is above average.\n";
    } elsif ($average = $_) {
        print "$_\t is equal to average.\n";
    }
}
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loop of the OPed code, the  elsif ($average = $_) { ... } clause of the ladder of if-tests does not work as I expect you expect. The  $average = $_ expression assigns to  $average and does not test it. (Update: An assignment of 0 evaluates as 0, which is boolean false.) The result is that for an element of 0 in the array, the body of that clause is not executed (update: because an assignment of 0 evaluates to 0, which is boolean false):

c:\@Work\Perl\monks>perl -wMstrict -le
"my @array = (-2, -1, 0, 1, 2);
 my $average = 0;
 ;;
 foreach (@array) {
   if ($average > $_) {
   print qq{$_\t is below average.};
   } elsif ($average < $_) {
       print qq{$_\t is above average.};
   } elsif ($average = $_) {
       print qq{$_\t is equal to average.};
   }
 }
"
-2       is below average.
-1       is below average.
1        is above average.
2        is above average.
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I assume you meant  $average == $_ as the test, although at that point the variables can only be equal (i.e., neither is greater nor less than the other), so a plain
    else {
        print "... equal to ...";
        }
would have been sufficient.

And another thing...
The code posted by pryrt for the  average() subroutine returns 0 for an empty list of numbers passed to the function.

c:\@Work\Perl\monks>perl -wMstrict -le
"print average();
 ;;
 sub average {
     if (@_) {
         my @temp = @_;
         my $sum = 0;
         foreach (@temp) {
             $sum = $sum + $_;
         }
         return $sum/@temp;
     }
 }
"
0
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I think I would have elected to return undef or perhaps throw an exception, but this behavior is the option of the programmer. However, one should be aware of it.