Moving Median, Mode in T-SQL - sql-server

Question

I am using SQL Server 2012 and I know it is quite simple to calculate moving averages.
But what I need is to get the mode and the median for a defined window frame like so (with a window of 2 preceding to current row; month unique):
MONTH | CODE | MEDIAN | MODE
1 0 0 0
2 3 1.5 0
3 2 2 0
4 2 2 2
5 2 2 2
6 5 2 2
7 3 3 2
If several values qualify as mode, than pick the first.

Answer 1

I commented my code thoroughly. Read my comments on my Mode calculations and let me know it needs tweaking. Overall, it's a relatively simple query. It just has a lot of ugly subqueries and it has a lot of comments. Check it out:
DECLARE #Table TABLE ([Month] INT,[Code] INT);
INSERT INTO #Table
VALUES (1,0),
(2,3),
(3,2),
(4,2), --Try commenting this out to test my special mode thingymajig
(5,2),
(6,5),
(7,3);
WITH CTE
AS
(
SELECT ROW_NUMBER() OVER (ORDER BY [Month]) row_num,
[Month],
CAST(Code AS FLOAT) Code
FROM #Table
)
SELECT [Month],
Code,
ISNULL((
SELECT CASE
--When there is only one previous value at row_num = 2, find Mean of first two codes
WHEN A.row_num = 2 THEN (LAG(B.code,1) OVER (ORDER BY [Code]) + B.Code)/2.0
--Else find middle code value of current and previous two rows
ELSE B.Code
END
FROM CTE B
--How subquery relates to outer query
WHERE B.row_num BETWEEN A.row_num - 2 AND A.row_num
ORDER BY B.[Code]
--Order by code and offset by 1 so don't select the lowest value, but fetch the one above the lowest value
OFFSET 1 ROW FETCH NEXT 1 ROW ONLY),
0) AS Median,
--I did mode a little different
--Instead of Avg(D.Code) you could list the values because with mode,
--If there's a tie with more than one of each number, you have multiple modes
--Instead of doing that, I simply return the mean of the tied modes
--When there's one, it doesn't change anything.
--If you were to delete the month 4, then your number of Codes 2 and number of Codes 3 would be the same in the last row.
--Proper mode would be 2,3. I instead average them out to be 2.5.
ISNULL((
SELECT AVG(D.Code)
FROM (
SELECT C.Code,
COUNT(*) cnt,
DENSE_RANK() OVER (ORDER BY COUNT(*) DESC) dnse_rank
FROM CTE C
WHERE C.row_num <= A.row_num
GROUP BY C.Code
HAVING COUNT(*) > 1) D
WHERE D.dnse_rank = 1),
0) AS Mode
FROM CTE A
Results:
Month Code Median Mode
----------- ---------------------- ---------------------- ----------------------
1 0 0 0
2 3 1.5 0
3 2 2 0
4 2 2 2
5 2 2 2
6 5 2 2
7 3 3 2

Answer 2

If I understood your requirements correctly, your source table contains MONTH and CODE columns, and you want to calculate MEDIAN and MODE.
The query below calculates MEDIAN and MODE with moving window <= than 3 month ("2 preceding to current row") and returns the results matching your example.
-----------------------------------------------------
--Demo data
-----------------------------------------------------
CREATE TABLE #Data(
[Month] INT NOT NULL,
[Code] INT NOT NULL,
CONSTRAINT [PK_Data] PRIMARY KEY CLUSTERED
(
[Month] ASC
));
INSERT #Data
([Month],[Code])
VALUES
(1,0),
(2,3),
(3,2),
(4,2),
(5,2),
(6,5),
(7,3);
-----------------------------------------------------
--Query
-----------------------------------------------------
DECLARE #PrecedingRowsLimit INT = 2;
WITH [MPos] AS
(
SELECT [R].[Month]
, [RB].[Month] AS [SubId]
, [RB].[Code]
, ROW_NUMBER() OVER(PARTITION BY [R].[Month] ORDER BY [RB].[Code]) AS [RowNumberInPartition]
, CASE
WHEN [R].[Count] % 2 = 1 THEN ([R].[Count] + 1) / 2
ELSE NULL
END AS [MedianPosition]
, CASE
WHEN [R].[Count] % 2 = 0 THEN [R].[Count] / 2
ELSE NULL
END AS [MedianPosition1]
, CASE
WHEN [R].[Count] % 2 = 0 THEN [R].[Count] / 2 + 1
ELSE NULL
END AS [MedianPosition2]
FROM
(
SELECT [RC].[Month]
, [RC].[RowNumber]
, CASE WHEN [RC].[Count] > #PrecedingRowsLimit + 1 THEN #PrecedingRowsLimit + 1 ELSE [RC].[Count] END AS [Count]
FROM
(
SELECT [Month]
, ROW_NUMBER() OVER(ORDER BY [Month]) AS [RowNumber]
, ROW_NUMBER() OVER(ORDER BY [Month]) AS [Count]
FROM #Data
) [RC]
) [R]
INNER JOIN #Data [RB]
ON [R].[Month] >= [RB].[Month]
AND [RB].[Month] >= [R].[RowNumber] - #PrecedingRowsLimit
)
SELECT DISTINCT [M].[Month]
, [ORIG].[Code]
, COALESCE([ME].[Code],([M1].[Code] + [M2].[Code]) / 2.0) AS [Median]
, [MOD].[Mode]
FROM [MPos] [M]
LEFT JOIN [MPOS] [ME]
ON [M].[Month] = [ME].[Month]
AND [M].[MedianPosition] = [ME].[RowNumberInPartition]
LEFT JOIN [MPOS] [M1]
ON [M].[Month] = [M1].[Month]
AND [M].[MedianPosition1] = [M1].[RowNumberInPartition]
LEFT JOIN [MPOS] [M2]
ON [M].[Month] = [M2].[Month]
AND [M].[MedianPosition2] = [M2].[RowNumberInPartition]
INNER JOIN
(
SELECT [MG].[Month]
, FIRST_VALUE([MG].[Code]) OVER (PARTITION BY [MG].[Month] ORDER BY [MG].[Count] DESC , [MG].[SubId] ASC) AS [Mode]
FROM
(
SELECT [Month] , MIN([SubId]) AS [SubId], [Code] , COUNT(1) AS [Count]
FROM [MPOS]
GROUP BY [Month] , [Code]
) [MG]
) [MOD]
ON [M].[Month] = [MOD].[Month]
INNER JOIN #Data [ORIG]
ON [ORIG].[Month] = [M].[Month]
ORDER BY [M].[Month];