This might be overkill but here's a way to do it using a DB_File in memory BTREE database. It works by inverting the original hash and allows for duplicate values (now keys) by setting the R_DUP flag. See the docs for how you would deal with duplicates:

use DB_File ;

my %hash = (
'-2.6' => 72,
'-2.5' => 165,
'-2.4' => 302,
'-2.3' => 168,
'-2.2' => 260,
'-2.1' => 151,
# ...etc.
);

$DB_BTREE->{'compare'} = sub { $_[0] <=> $_[1] };
$DB_BTREE->{'flags'} = R_DUP;
my %h;
my $db = tie %h, "DB_File", undef, undef, undef, $DB_BTREE;

while (my($k,$v) = each %hash) {
    $h{$v} = $k;
}

my ($key,$value,$half);
# get the max
$db->seq($key, $value, R_LAST);
print "Max: $key -> $value\n";
$key = $half = $key / 2;
# get the nearest to half
$db->seq($key, $value, R_CURSOR);
print "$key -> $value\n";
$key <= $half ? $db->seq($key, $value, R_NEXT)
              : $db->seq($key, $value, R_PREV);
print "$key -> $value\n";
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Output:

Max: 302 -> -2.4
151 -> -2.1
165 -> -2.5
[download]