Average and Median in one query in Sql Server 2012

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.

1. To get average:

     SELECT category, avg(value) as Average
       FROM test
   GROUP BY category
   

    
    | category | value |
    +----------+-------+
    |    1     |   4   | 
    

2. 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