Postgres 14

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create table prod (product varchar(1), quantity integer, constraint pk primary key (product, quantity)) ;

insert into prod values
('A',	1),
('A',	2),
('A',	3),
('B',	5),
('B',	6),
('B',	7),
('C',	11),
('C',	13),
('C',	15),
('D',	4),
('D',	5),
('D',	6)
12 rows affected

SELECT DISTINCT ON (t.Product)
       t.Product
     , nth_value(t.Quantity, m.median) OVER (PARTITION BY t.Product ORDER BY Quantity ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING) AS median_Qty
  FROM prod AS t
 INNER JOIN
     ( SELECT Product, round(count(*)/2+1) :: integer AS median
         FROM prod
        GROUP BY Product
     ) AS m
    ON m.Product = t.Product


product
median_qty


A
2

B
6

C
13

D
5


CREATE OR REPLACE FUNCTION median_quantity(INOUT Product varchar(1), OUT Median_Quantity integer)
RETURNS setof record LANGUAGE plpgsql AS
$$
DECLARE
  median integer ;
BEGIN
    SELECT round(count(*)/2) :: integer
      INTO median
      FROM prod
     GROUP BY prod.Product ;
     
    RETURN QUERY EXECUTE E'
    SELECT Product, Quantity
      FROM prod
     WHERE Product = ' || quote_nullable(Product) || '
     ORDER BY Quantity
     LIMIT 1
     OFFSET ' || median ;
END ;
$$ ;
SELECT m.Product, m.Median_Quantity
  FROM 
     ( SELECT DISTINCT ON (Product)
              Product
         FROM prod
     ) AS p
 CROSS JOIN LATERAL median_quantity(p.Product) AS m
 


product
median_quantity


A
2

B
6

C
13

D
5