Assuming that performance is not your main concern and that your data really is bell-shaped (in particular increasing up to the max, and then decreasing), the following should do the trick:

my $max = max values %hash;
my $half = $max/2;
my @above = grep { $hash{$_} >= $half } keys %hash;
my $keylo = min @above;
my $keyhi = max @above;

print "1: $max\n";
print "2: $half\n";
print "3: $keylo, $keyhi\n";
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If you need the closest, you might want to check the neighbors of $keylo and $keyhi as well.