This turns out to be pretty easy.  You might also want to read Implementing Harmonic Mean in MySQL.

Why bother blogging something this simple?  Because I couldn’t find one pre-made, and that means it’s time to bring my mighty google rank of like negative two to bear to fix the problem.

CREATE TABLE example(val integer);
INSERT INTO example VALUES(1),(2),(4),(8),(16);
SELECT exp(avg(ln(val))) as gmean from example;

That’s it.  You should see output like this:

mysql> CREATE TABLE example(val integer);
Query OK, 0 rows affected (0.09 sec)

mysql> INSERT INTO example VALUES(1),(2),(4),(8),(16);
Query OK, 5 rows affected (0.01 sec)
Records: 5  Duplicates: 0  Warnings: 0

mysql> SELECT exp(avg(ln(val))) as gmean from example;
+- - - -+
| gmean |
+- - - -+
|     4 |
+- - - -+
1 row in set (0.00 sec)

Still haven’t figured out how to do central moments, skewness or kurtosis.