CREATE TABLE `products` (
  `id` int(11) NOT NULL,
  `price` float DEFAULT NULL,
  PRIMARY KEY (`id`),
  KEY `price` (`price`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1

select id, price from products a 
join (select min(price) mi , max(price) ma from products )  b 
WHERE a.price >= (b.mi +b.ma)/2 limit 1;

mysql> select count(*) from products;
+----------+
| count(*) |
+----------+
|    10000 |
+----------+
1 row in set (0.00 sec)

mysql> select id, price from products a join (select min(price) mi , max(price) ma from products )  b WHERE a.price >= (b.mi +b.ma)/2 limit 1;
+------+----------+
| id   | price    |
+------+----------+
| 4123 | 0.500079 |
+------+----------+
1 row in set (0.00 sec)


mysql> show status like 'Hand%';
+----------------------------+-------+
| Variable_name              | Value |
+----------------------------+-------+
| Handler_commit             | 1     |
| Handler_delete             | 0     |
| Handler_discover           | 0     |
| Handler_prepare            | 0     |
| Handler_read_first         | 1     |
| Handler_read_key           | 3     |
| Handler_read_last          | 1     |
| Handler_read_next          | 0     |
| Handler_read_prev          | 0     |
| Handler_read_rnd           | 0     |
| Handler_read_rnd_next      | 1     |
| Handler_rollback           | 0     |
| Handler_savepoint          | 0     |
| Handler_savepoint_rollback | 0     |
| Handler_update             | 0     |
| Handler_write              | 1     |
+----------------------------+-------+
16 rows in set (0.00 sec)