SQL Server 2022

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Microsoft SQL Server 2022 (RTM) - 16.0.1000.6 (X64) Oct 8 2022 05:58:25 Copyright (C) 2022 Microsoft Corporation Express Edition (64-bit) on Windows Server 2019 Standard 10.0 <X64> (Build 17763: ) (Hypervisor)

drop table if exists #data;

create table #data (
  id int,
  "Transaction" nvarchar(10),
  amount int,
  inventory int,
  price int
);

insert into #data(id, "Transaction", amount, inventory, price)
  values
    (1, NULL, NULL, 11, NULL),
    (2, 'Sale', -1, 10, 100),
    (3, 'Purchase', 2, 12, 102),
    (4, 'Sale', -2, 10, 103);

drop table if exists #averages;

create table #averages (
  id int,
  "Transaction" nvarchar(10),
  amount int,
  inventory int,
  price int,
  average float
);

declare
  @id int,
  @tran nvarchar(10),
  @amt int,
  @inv int,
  @price int,
  @avg float;

DECLARE C CURSOR FORWARD_ONLY STATIC READ_ONLY FOR
  select *
  from #data
  order by id;

open c;

FETCH NEXT FROM C INTO @id, @tran, @amt, @inv, @price;

WHILE @@FETCH_STATUS = 0 BEGIN
  set @avg = case
               when @tran is null then 90
               else
                 case @tran
                   when 'Sale' then @avg
                   else (@avg * (@inv - @amt) +
                         @amt * @price) / @inv
                 end
             end;
  insert into #averages(id, "Transaction", amount, inventory, price, average)
    values(@id, @tran, @amt, @inv, @price, @avg);
  FETCH NEXT FROM C INTO @id, @tran, @amt, @inv, @price;
END;

CLOSE C;
DEALLOCATE C;

select * from #averages;

id	Transaction	amount	inventory	price	average
1	null	null	11	null	90
2	Sale	-1	10	100	90
3	Purchase	2	12	102	92
4	Sale	-2	10	103	92