PostgreSQL Query: Column Sum for the latest available date of each month - postgresql

Question

Given a pSQL table which looks like this:
date | data
2015-01-23 | 15
2015-01-23 | 11
2015-02-25 | 15
2015-02-25 | 11
2015-01-25 | 24
2015-01-25 | 2
2015-01-25 | 13
2015-01-29 | 5
2015-02-28 | 12
2015-02-28 | 1
2015-05-15 | 12
2015-05-16 | 1
How can I get the sum of data for the last available date of each month?
Example result:
date | data
2015-01-29 | 5
2015-02-28 | 13
2015-05-16 | 1
This is what I've tried so far:
SELECT year,month,max(day),sum(data) FROM
(
SELECT
date,
date_part('year', date) AS year,
date_part('month', date) AS month,
date_part('day', date) AS day,
sum(data) AS tdata
FROM table a
GROUP BY date, date_part('year', date), date_part('month', date), date_part('day', date)
ORDER BY year ASC, month ASC, day ASC
) dataq
GROUP BY year,month
The sum I get from this appears to be wrong.

Answer 1

You should calculate the sums in the inner query, grouping by a single day. Select latest day in month in the outer query:
select distinct on (year, month)
make_date(year::int, month::int, day::int) as date,
data
from (
select
date_part('year', date) as year,
date_part('month', date) as month,
date_part('day', date) as day,
sum(data) as data
from my_table
group by date
) s
order by year, month, day desc
date | data
------------+------
2015-01-29 | 5
2015-02-28 | 13
2015-05-16 | 1
(3 rows)

Answer 2

I guess you need just to remove days that you don't want to sum. For example using NOT EXISTS as follows:
SELECT year,month,max(day),sum(tdata) tdata FROM
(
SELECT
d,
date_part('year', d) AS year,
date_part('month', d) AS month,
date_part('day', d) AS day,
sum(data) AS tdata
FROM tab a
WHERE NOT EXISTS
(
SELECT *
FROM tab a2
WHERE date_part('year', a.d) = date_part('year', a2.d) AND
date_part('month', a.d) = date_part('month', a2.d) AND
date_part('day', a.d) < date_part('day', a2.d)
)
GROUP BY d, date_part('year', d), date_part('month', d), date_part('day', d)
ORDER BY year ASC, month ASC, day ASC
) dataq
GROUP BY year,month
SQLFiddle