If that still wasn't fast enough, this one should blow the doors off of both.

SELECT a.[Contract], a.AdmissionDate, Cost=SumofCost, Members=CountofMembers

,SumofCost=CAST(0.0 AS DECIMAL(19,4))

,CountofMembers=0

,AvgCost=CAST(0.0 AS DECIMAL(19,4))

INTO #NewTable

FROM Members a

JOIN Admission b ON a.[Contract] = b.[Contract] AND

a.AdmissionDate = b.AdmissionDate

ALTER TABLE #NewTable ALTER COLUMN AdmissionDate VARCHAR(6) NOT NULL;

ALTER TABLE #NewTable ADD PRIMARY KEY(AdmissionDate);

DECLARE @Lag1SOC DECIMAL(19, 4) = 0

,@Lag2SOC DECIMAL(19, 4) = 0

,@Lag3SOC DECIMAL(19, 4) = 0

,@Lag1CM INT = 0

,@Lag2CM INT = 0

,@Lag3CM INT = 0

,@rtSOC DECIMAL(19, 4) = 0

,@rtCM INT = 0

,@rn INT = 0;

UPDATE #NewTable WITH(TABLOCKX)

SET @rtSOC = SumOfCost = @rtSOC + Cost - @Lag3SOC

,@rtCM = CountOfMembers = @rtCM + Members - @Lag3CM

,AvgCost = CASE WHEN @rn < 3 THEN NULL

WHEN @rtCM = 0 THEN 0

ELSE @rtSOC / @rtCM

END

,@Lag3SOC = @Lag2SOC

,@Lag2SOC = @Lag1SOC

,@Lag1SOC = Cost

,@Lag3CM = @Lag2CM

,@Lag2CM = @Lag1CM

,@Lag1CM = Members

,@rn = @rn + 1

OPTION (MAXDOP 1);

SELECT [Contract], AdmissionDate, SumofCost, CountofMembers, AvgCost

FROM #NewTable;

GO

DROP TABLE #NewTable;

Understanding how the Quirky Update (QU) works and all the rules can be a bit of a challenge, but this article by SQL MVP Jeff Moden goes into all the details:

Solving the Running Total and Ordinal Rank Problems[/url]

While the article covers only running totals, what I've done here is to limit the running totals to the current + prior 2 rows using the @lag variables.