Calculating a median value

A median is a numerical value that separates the higher half of a sample from the lower half. For example, you can retrieve the median of a finite list of numbers by arranging all observations from lowest value to highest value and then picking the middle one.

If the number of observations is even, then there is no single middle value; the median is the mean (average) of the two middle values.

The following example uses this table:

CREATE TABLE allsales(state VARCHAR(20), name VARCHAR(20), sales INT);
INSERT INTO allsales VALUES('MA', 'A', 60);
INSERT INTO allsales VALUES('NY', 'B', 20);
INSERT INTO allsales VALUES('NY', 'C', 15);
INSERT INTO allsales VALUES('MA', 'D', 20);
INSERT INTO allsales VALUES('MA', 'E', 50);
INSERT INTO allsales VALUES('NY', 'F', 40);
INSERT INTO allsales VALUES('MA', 'G', 10);
COMMIT;

You can use the analytic function MEDIAN to calculate the median of all sales in this table. In the following query, the function's OVER clause is empty, so the query returns the same aggregated value for each row of the result set:

=> SELECT name, sales, MEDIAN(sales) OVER() AS median FROM allsales;
 name | sales | median
------+-------+--------
 G    |    10 |     20
 C    |    15 |     20
 D    |    20 |     20
 B    |    20 |     20
 F    |    40 |     20
 E    |    50 |     20
 A    |    60 |     20
(7 rows)

You can modify this query to group sales by state and obtain the median for each one. To do so, include a window partition clause in the OVER clause:

=> SELECT state, name, sales, MEDIAN(sales) OVER(partition by state) AS median FROM allsales;
 state | name | sales | median
-------+------+-------+--------
 MA    | G    |    10 |     35
 MA    | D    |    20 |     35
 MA    | E    |    50 |     35
 MA    | A    |    60 |     35
 NY    | C    |    15 |     20
 NY    | B    |    20 |     20
 NY    | F    |    40 |     20
(7 rows)