How to write an sql-query for grouping by conditions: more than the average value, less than the average value?

Question

PostgreSQL

Table

grp | val | date
------------------------
t     |   1   |   01-01-1990
f     |   3   |   02-01-1990
t     |   2   |   03-01-1990
f     |   2  |   02-01-1990
f     |   1  |   02-01-1990

You need to get a table like this:

Промежуток           | t | f | sum строк
--------------------------------------------------
больше среднего val | 2 | 2,5 | 2
меньше среднего val | 1 | 1   | 1
--------------------------------------------------
итого              |  2  | 3  | 5

The totals are the number of lines grouped by grp and total.