I need an sql statement

I have a table that contains several fields. I am going to use only three of the aggregate fields here. My SQL statement is:

select user_id, position_id, avg(g), avg(a), avg(p) from 1_f_pg_mod where user_id = 6 group by position_id;

This gives:
user_id      position_id                avg(g)                      avg(a)                        avg(p)
6                    2                  20.348837209302        28.720930232558        49.06976744186
6                    1               17.640845070423                31.514084507042        49.154929577465
6                    3                 20.919540229885        27.931034482759        48.850574712644

What I want to achieve is to get the average of all the positions joined up and call it say 4. The results would look something like (obviously the numbers are not right):
user_id      position_id                          avg(g)                                 avg(a)                 avg(p)
6      (Joined position 1,2 and 3=4)      20.348837209302      28.720930232558      49.06976744186

This is a touch difficult to explain but hope you get the drift.

Thank you.