Group by school year in postgres - postgresql

Question

I have a query where I count the number of rows for each year:
SELECT
count(*) as activation_count
, extract(year from activated_at) as year
FROM "activations"
WHERE ...
GROUP BY year
But I'd like instead to have years ranging from September to September instead of January to January. Thus grouping by school years instead of calendar years.
Can I modify my query to do that?
And more generally, is it possible to group by a time range and specify an offset to it, eg: extract(year from activated_at offset interval 2 month) as year (this is not working, just the idea of what I want)

Answer 1

What you essentially want is to treat all dates after September as "next year", so the following should work:
select count(*) as activation_count,
case
when extract(month from activated_at) >= 9 then extract(year from activated_at) + 1
else extract(year from activated_at)
end as school_year
from activations
group by school_year;

Answer 2

Assuming that someone whose activated_at is '2016-09-01' should be counted as year = 2017, you could add 4 months to activated_at when in the extract (translating (in the mathematical sense of the word) September to January).
SELECT * FROM activations ;
┌────────────────────────┐
│ activated_at │
├────────────────────────┤
│ 2016-08-01 00:00:00+02 │
│ 2016-09-01 00:00:00+02 │
│ 2016-10-01 00:00:00+02 │
│ 2017-02-02 00:00:00+01 │
└────────────────────────┘
(4 rows)
SELECT COUNT(*),
EXTRACT(year FROM (activated_at + '4 months'::interval)) AS year
FROM activations
GROUP BY year;
┌───────┬──────┐
│ count │ year │
├───────┼──────┤
│ 3 │ 2017 │
│ 1 │ 2016 │
└───────┴──────┘
(2 rows)
If it should be counted as year = 2016 you could remove 8 months instead.