SQL Server 2019

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CREATE TABLE tableA( input_date datetime,
                     output_date datetime,
                     processing_time int);

INSERT INTO tableA VALUES ('2022-01-03', '2022-01-03', 0),
                          ('2022-01-03', '2022-01-06', 3),
                          ('2022-01-03', '2022-01-11', 8),
                          ('2022-01-05', '2022-01-10', 5),
                          ('2022-01-05', '2022-01-15', 10);
5 rows affected

select * from tableA


input_date
output_date
processing_time


2022-01-03 00:00:00.000
2022-01-03 00:00:00.000
0

2022-01-03 00:00:00.000
2022-01-06 00:00:00.000
3

2022-01-03 00:00:00.000
2022-01-11 00:00:00.000
8

2022-01-05 00:00:00.000
2022-01-10 00:00:00.000
5

2022-01-05 00:00:00.000
2022-01-15 00:00:00.000
10


with cte as (
select input_date,
       PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY processing_time) OVER(PARTITION BY input_date) as Median_Process_Time
FROM tableA
)

SELECT *
FROM cte
GROUP BY input_date, Median_Process_Time


input_date
Median_Process_Time


2022-01-03 00:00:00.000
3

2022-01-05 00:00:00.000
7.5

input_date	output_date	processing_time
2022-01-03 00:00:00.000	2022-01-03 00:00:00.000	0
2022-01-03 00:00:00.000	2022-01-06 00:00:00.000	3
2022-01-03 00:00:00.000	2022-01-11 00:00:00.000	8
2022-01-05 00:00:00.000	2022-01-10 00:00:00.000	5
2022-01-05 00:00:00.000	2022-01-15 00:00:00.000	10