SQL Server 2019

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CREATE TABLE example_cumulative
(batch_id INT NOT NULL, 
 item_id  INT NOT NULL, 
 cost     FLOAT NOT NULL
);
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,10,100)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,11,100)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,12,106)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,13,142)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,14,152)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (1,15,154)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (2,10,110)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (2,11,140)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (2,12,100)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (2,16,100)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (3,10,110)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (3,11,100)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (3,16,195)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (3,17,102)
INSERT INTO example_cumulative (batch_id, item_id, cost) VALUES (3,18,101)

15 rows affected

batch_id	new_items	removed_items	net_change
1	6	0	6
2	1	3	-2
3	2	1	1

Warning: Null value is eliminated by an aggregate or other SET operation.