How to do While Loops?

Question

How can we use while loops in MySQL? My test script:

BEGIN
    SELECT 0 INTO @n;
    WHILE @n < 10 DO
    SELECT @n;
    SET @n := @n +1;
    END WHILE;
END;

But it has syntax errors. I'm running the loop using the SQLyog client in a standard query window. The syntax errors are of the following form:

Error Code: 1064
You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near...

I've also tried to use the while loop example provided by https://dev.mysql.com/doc/refman/5.6/en/while.html but it still didn't work.

Which part of the script is wrong? (Using MySQL 5.6.)

I'm trying to make a 6 month moving average of some data so I was hoping that a while loop would be able to append the "new" 6 month average onto the "old" 6 month average through each iteration of the loop.