Average and Median in one query in Sql Server 2012 - sql

Question

I have the following data in my table:
SELECT category, value FROM test
| category | value |
+----------+-------+
| 1 | 1 |
| 1 | 3 |
| 1 | 4 |
| 1 | 8 |
Right now I am using two separate queries.
To get average:
SELECT category, avg(value) as Average
FROM test
GROUP BY category
| category | value |
+----------+-------+
| 1 | 4 |
To get median:
SELECT DISTINCT category,
PERCENTILE_CONT(0.5)
WITHIN GROUP (ORDER BY value)
OVER (partition BY category) AS Median
FROM test
| category | value |
+----------+-------+
| 1 | 3.5 |
Is there any way to merge them in one query?
Note: I know that I can also get median with two subqueries, but I prefer to use PERCENTILE_CONT function to get it.

Answer 1

AVG is also a windowed function:
select
distinct
category,
avg(value) over (partition by category) as average,
PERCENTILE_CONT(0.5)
WITHIN GROUP (ORDER BY value)
OVER (partition BY category) AS Median
from test

Answer 2

I would approach this in a slightly different way:
select category, avg(value) as avg,
avg(case when 2 * seqnum in (cnt, cnt + 1, cnt + 2) then value end) as median
from (select t.*, row_number() over (partition by category order by value) as seqnum,
count(*) over (partition by category) as cnt
from test t
) t
group by category;

Answer 3

I wanted a more thorough answer to this question, and after some digging found it in this exhaustive analysis of multiple methods from Dwain Camps, in case others find it useful:
Calculating the Median Value within a Partitioned Set Using T-SQL
I went with "his" 4th solution (he is combining/testing others' approaches), which was straightforward to understand and indeed performs well:
WITH Counts AS
(
SELECT ID, c=COUNT(*)
FROM #MedianValues
GROUP BY ID
)
SELECT a.ID, Median=AVG(0.+N)
FROM Counts a
CROSS APPLY
(
SELECT TOP(((a.c - 1) / 2) + (1 + (1 - a.c % 2)))
N, r=ROW_NUMBER() OVER (ORDER BY N)
FROM #MedianValues b
WHERE a.ID = b.ID
ORDER BY N
) p
WHERE r BETWEEN ((a.c - 1) / 2) + 1 AND (((a.c - 1) / 2) + (1 + (1 - a.c % 2)))
GROUP BY a.ID;