Bin into groups of equal size

CREATE TABLE orders AS SELECT * FROM (VALUES
  (1,  'Alice Ng',      'north', DATE '2026-01-03', 120.00, 'widget', 'a|b',   '{"channel":"web","items":[1,2]}'),
  (2,  'alice ng',      'north', DATE '2026-01-05',  80.50, 'gadget', 'b',     '{"channel":"shop","items":[3]}'),
  (3,  'Bob  Okafor',   'south', DATE '2026-01-05', 300.00, 'widget', 'a|c',   '{"channel":"web","items":[4,5,6]}'),
  (4,  'Carla Díaz',    'east',  DATE '2026-01-09',  NULL,  'gizmo',  NULL,    '{"channel":"web","items":[]}'),
  (5,  'Bob Okafor',    'south', DATE '2026-01-12',  45.25, 'gadget', 'c',     '{"channel":"phone","items":[7]}'),
  (6,  'Dev Patel',     'west',  DATE '2026-01-12', 510.00, 'widget', 'a',     '{"channel":"web","items":[8,9]}'),
  (7,  'Carla Diaz',    'east',  DATE '2026-01-20',  99.99, 'gizmo',  'b|c',   '{"channel":"shop","items":[10]}'),
  (8,  'Dev Patel',     'west',  DATE '2026-02-02', 510.00, 'widget', 'a',     '{"channel":"web","items":[8,9]}'),
  (9,  'Eve Larsen',    NULL,    DATE '2026-02-03',  15.00, 'gadget', NULL,    '{"channel":"web","items":[11]}'),
  (10, 'Alice Ng',      'north', DATE '2026-02-10', 220.00, 'gizmo',  'a|b|c', '{"channel":"phone","items":[12,13]}')
) t(order_id, customer, region, order_date, amount, product, tags, meta);

-- the missing amount is ranked in a partition of its own and then given no quartile, so it keeps its row without shifting the others
CREATE TEMP TABLE result AS
SELECT order_id, amount,
       CASE WHEN amount IS NOT NULL THEN ntile(4) OVER (PARTITION BY amount IS NULL ORDER BY amount) END AS quartile FROM orders;
SELECT * FROM result ORDER BY amount;
SELECT CASE WHEN ((SELECT count(*) FROM result) = 10 AND (SELECT quartile FROM result WHERE order_id = 4) IS NULL AND (SELECT list(n ORDER BY quartile) FROM (SELECT quartile, count(*) AS n FROM result WHERE quartile IS NOT NULL GROUP BY quartile)) = [3, 2, 2, 2] AND (SELECT quartile FROM result WHERE order_id = 9) = 1 AND (SELECT quartile FROM result WHERE order_id = 1) = 2 AND (SELECT quartile FROM result WHERE order_id = 7) = 2 AND (SELECT quartile FROM result WHERE order_id = 10) = 3 AND (SELECT min(quartile) FROM result WHERE amount = 510) = 4 AND (SELECT max(quartile) FROM result WHERE amount = 510) = 4) THEN 'as expected' ELSE error('the nine amounts were not dealt into four quartiles of 3, 2, 2 and 2 rows in order with the missing amount kept and unbinned') END AS verdict;