dan@dan:~$ mysql sandbox
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 19
Server version: 5.0.37 MySQL Community Server (GPL)
 
Type 'help;' or '\h' for help. Type '\c' to clear the buffer.
 
mysql> create table some_table (foo int(11), bar int(11));
Query OK, 0 rows affected (0.01 sec)
 
mysql> insert into some_table (foo, bar) values (1, 2), (3, 4), (5, 6), (7, 8);
Query OK, 4 rows affected (0.00 sec)
Records: 4  Duplicates: 0  Warnings: 0
 
mysql> explain select avg(foo) from some_table group by bar;
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
| id | select_type | table      | type | possible_keys | key  | key_len | ref  | rows | Extra                           |
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
|  1 | SIMPLE      | some_table | ALL  | NULL          | NULL | NULL    | NULL |    4 | Using temporary; Using filesort | 
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
1 row in set (0.00 sec)
 
mysql> create index index_bar on some_table (bar);
Query OK, 4 rows affected (0.02 sec)
Records: 4  Duplicates: 0  Warnings: 0
 
mysql> explain select avg(foo) from some_table group by bar;
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
| id | select_type | table      | type | possible_keys | key  | key_len | ref  | rows | Extra                           |
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
|  1 | SIMPLE      | some_table | ALL  | NULL          | NULL | NULL    | NULL |    4 | Using temporary; Using filesort | 
+----+-------------+------------+------+---------------+------+---------+------+------+---------------------------------+
1 row in set (0.00 sec)
 
mysql> create index index_bar_foo on some_table (bar, foo);
Query OK, 4 rows affected (0.01 sec)
Records: 4  Duplicates: 0  Warnings: 0
 
mysql> explain select avg(foo) from some_table group by bar;
+----+-------------+------------+-------+---------------+---------------+---------+------+------+-------------+
| id | select_type | table      | type  | possible_keys | key           | key_len | ref  | rows | Extra       |
+----+-------------+------------+-------+---------------+---------------+---------+------+------+-------------+
|  1 | SIMPLE      | some_table | index | NULL          | index_bar_foo | 10      | NULL |    4 | Using index | 
+----+-------------+------------+-------+---------------+---------------+---------+------+------+-------------+
1 row in set (0.00 sec)