Median over time - SQL Server - sql

Question

I have data (support ticket statistics, to be exact), that I am trying to get the median of, over time.
Right now, I have a query that calculates the difference between the date the ticket was opened and the date it was closed. I take that data and pivot the average of the days to close over a series of months and years, using SQL Servers built in AVG function. This works well, however I am finding that the metrics are skewed due to outliers in the data.
What I really want, is the Median of the data, pivoted over months and years. I am having trouble achieving what I am after, and I am not positive if this is even possible.
The query I have right now, using the AVG function, is:
SELECT 'Support - Days To Close Escalation', *
FROM
(
SELECT
DATEDIFF(HOUR, e.CreatedDate, e.Escalation_Close_Date_Time__c) AS DaysToCloseEscalation,
LEFT(CONVERT(CHAR(10), e.CreatedDate,126), 7) AS EscalationCreateDate
FROM [dbo].[Escalations] AS e WITH(NOLOCK)
LEFT JOIN [dbo].[Case] AS c WITH(NOLOCK)
ON e.Case__c = c.Id
WHERE e.Escalation_Queue__c IN ('PM 10 Tier 2 Support', 'PM 11 Tier 2 Support')
AND e.CreatedDate BETWEEN '2017-04-01 00:00:00.000' AND '2018-04-01 00:00:00.000'
AND e.Escalation_Close_Date_Time__c IS NOT NULL
) AS SupportEscalationVolume
PIVOT
(
AVG(SupportEscalationVolume.DaysToCloseEscalation) FOR SupportEscalationVolume.EscalationCreateDate IN ([2017-04],[2017-05],[2017-06],[2017-07],[2017-08],[2017-09],[2017-10],[2017-11],[2017-12],[2018-01],[2018-02],[2018-03])
) AS SupportEscalationVolumePivot
The result of this query is something along the lines of (except all in a single row, since the data is pivoted):
StatDescription | Support - Days To Close Escalation
----------------------------------------------------
2017-04 | 107
2017-05 | 52
2017-06 | 101
2017-07 | 106
2017-08 | 69
2017-09 | 54
2017-10 | 49
2017-11 | 42
2017-12 | 51
2018-01 | 31
2018-02 | 23
2018-03 | 15
After some research on how to pull of a Median in SQL, I have resorted to using DENSE_RANK(), as shown in the query below. I started with ROW_NUMBER(), but that gave me a counter for ALL records, where what I really want is a median of the time to close the ticket for each month/year grouping.
;
WITH SupportDaysToClose(HoursToCloseEscalation, EscalationCreateDate, RowNumber)
AS
(
SELECT
DATEDIFF(HOUR, e.CreatedDate, e.Escalation_Close_Date_Time__c) AS HoursToCloseEscalation,
LEFT(CONVERT(CHAR(10), e.CreatedDate,126), 7) AS EscalationCreateDate,
DENSE_RANK() OVER(ORDER BY LEFT(CONVERT(CHAR(10), e.CreatedDate,126), 7) ASC) AS RowNumber
FROM [dbo].[Escalations] AS e WITH(NOLOCK)
LEFT JOIN [dbo].[Case] AS c WITH(NOLOCK)
ON e.Case__c = c.Id
WHERE e.Escalation_Queue__c IN ('PM 10 Tier 2 Support', 'PM 11 Tier 2 Support')
AND e.CreatedDate BETWEEN '2017-04-01 00:00:00.000' AND '2018-04-01 00:00:00.000'
AND e.Escalation_Close_Date_Time__c IS NOT NULL
)
SELECT *
FROM SupportDaysToClose
ORDER BY RowNumber,HoursToCloseEscalation
A sample of this data looks like
HoursToClose|CreateDate|RowNumber
---------------------------------
0 |2017-04 |1
7 |2017-08 |5
27 |2017-12 |9
Each RowNumber correlates to a given month and year, the maximum being at 12.
At this point, I am not really sure where to go.
Has anyone ever done anything like this before? I am not sure if I am on the right track or if I need to rethink the whole strategy. I apologize in advance if the syntax is difficult to follow.