Is there a better way to calculate the median (not average)

Question

Suppose I have the following table definition:

CREATE TABLE x (i serial primary key, value integer not null);

I want to calculate the MEDIAN o

Answer 1

A simpler query for that:

WITH y AS (
   SELECT value, row_number() OVER (ORDER BY value) AS rn
   FROM   x
   WHERE  value IS NOT NULL
   )
, c AS (SELECT count(*) AS ct FROM y) 
SELECT CASE WHEN c.ct%2 = 0 THEN
          round((SELECT avg(value) FROM y WHERE y.rn IN (c.ct/2, c.ct/2+1)), 3)
       ELSE
                (SELECT     value  FROM y WHERE y.rn = (c.ct+1)/2)
       END AS median
FROM   c;

Major points

• Ignores NULL values.
• Core feature is the row_number() window function, which has been there since version 8.4
• The final SELECT gets one row for uneven numbers and avg() of two rows for even numbers. Result is numeric, rounded to 3 decimal places.

Test shows, that the new version is 4x faster than (and yields correct results, unlike) the query in the question:

CREATE TEMP TABLE x (value int);
INSERT INTO x SELECT generate_series(1,10000);
INSERT INTO x VALUES (NULL),(NULL),(NULL),(3);