SQL Server 2019

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with CTE_data as ( --Your original data
    SELECT * FROM ( VALUES 
        ('SW', 'Phoenix', CONVERT(DATE,'2021-10-01'), CONVERT(DECIMAL(18,6),'400'))
        , ('NE', 'Boston', '2021-10-03', '20')
        , ('SW', 'Phoenix', '2021-10-03', '800')
        , ('SW', 'Phoenix', '2021-10-02', '425')
        , ('NE', 'Boston', '2021-10-01', '500')
        , ('SW', 'Phoenix', '2021-10-02', '15')
        , ('SW', 'Phoenix', '2021-10-04', '100')
        , ('NE', 'Boston', '2021-10-04', '35')
    ) as TabA(Region, City, ReadingDate, Amount) 
), cteStats as ( --Calculate the Avg & Std of the raw data
    SELECT 
         *
        ,AVG(Amount) OVER (PARTITION BY Region, City) AS AvgRaw
        ,STDEV(Amount) OVER (PARTITION BY Region, City) AS StedRaw
    FROM CTE_data
)
SELECT 
         S.Region
        ,S.City
        ,MIN(CASE WHEN s.Amount BETWEEN S.AvgRaw - S.StedRaw AND S.AvgRaw + S.StedRaw 
               THEN S.ReadingDate END) AS MinDate
        ,MAX(CASE WHEN s.Amount BETWEEN S.AvgRaw - S.StedRaw AND S.AvgRaw + S.StedRaw 
               THEN S.ReadingDate END) AS MaxDate
        ,AVG(CASE WHEN s.Amount BETWEEN S.AvgRaw - S.StedRaw AND S.AvgRaw + S.StedRaw 
               THEN S.Amount END) AS AvgFiltered
        ,AVG(S.Amount) AS AvgAll
FROM cteStats as S
GROUP BY s.Region, S.City;

Region	City	MinDate	MaxDate	AvgFiltered	AvgAll
NE	Boston	2021-10-03	2021-10-04	27.500000	185.000000
SW	Phoenix	2021-10-01	2021-10-04	308.333333	348.000000

Warning: Null value is eliminated by an aggregate or other SET operation.