Finally dug up Itzik's book on T-SQL 2008...

-- from p.458 "Inside SQL Server 2008 T-SQL Querying" By Itzik Ben-Gan

SELECT 01.empID,

CONVERT(VARCHAR(7), o1.ordMonth, 121) AS toMonth,

o1.qty AS qtyThisMonth,

SUM(o2.qty) AS totalQty,

CAST(AVG(1 * o2.qty) AS NUMERIC(12,2)) AS avgQty

FROM dbo.EmpOrders AS o1

JOIN dbo.EmpOrders o2

ON o2.empID = 01.empID

AND (02.ordmonth > DATEADD(month, -3, o1.ordMonth)

AND o2.ordMonth <= o1.ordMonth)

GROUP BY o1.empID, o1.ordMonth, o1.qty

ORDER BY o1.empID, o1.ordMonth;

Tweaking IBG's solution to your structure...

SELECT x1.username

, x1.move_in_date

, SUM(x2.cnt_lead_id) as totalqty

, CAST(AVG(1 * x2.cnt_lead_id) aS NUMERIC(12,2)) AS avgQty

FROM dbo.countHistory x1

JOIN dbo.countHistory x2

ON x2.username = x1.username

AND x2.move_in_date<=x1.move_in_date

GROUP BY x1.username, x1.move_in_date, x1.cnt_lead_id

ORDER BY x1.username, x1.move_in_date;

I think that's right... but anything involving my brain and T-SQL at 4AM could hardly be called "thinking".