For two sums and three medians, on a single table, I honestly can't see the benefit of using a complicated dynamic or function-based solution.

It is quite easy to construct a single query using Peter Larsson's median method that I showed you before:

CREATE TABLE dbo.Listing
(
    ListingCol1 integer NULL,
    ListingCol2 integer NULL,
    ListingCol3 integer NULL,
    ListingCol4 integer NULL,
    ListingCol5 integer NULL
);

CREATE TABLE dbo.Result
(
    Col1 integer NULL,
    Col2 integer NULL,
    Col3 integer NULL,
    Col4 integer NULL,
    Col5 integer NULL
);

-- Just to show indexes are helpful for the median calculations
CREATE INDEX i ON dbo.Listing (ListingCol3)
CREATE INDEX j ON dbo.Listing (ListingCol4)
CREATE INDEX k ON dbo.Listing (ListingCol5)

###Solution

INSERT dbo.Result
(
    Col1,
    Col2,
    Col3,
    Col4,
    Col5
)
SELECT
    SC.SumCol1,
    SC.SumCol2,
    SQ3.MedianCol3,
    SQ4.MedianCol4,
    SQ5.MedianCol5
FROM 
(
    -- Sums + counts needed for the median calculations
    SELECT 
        SumCol1 = SUM(L.ListingCol1),
        SumCol2 = SUM(L.ListingCol2),
        CountCol3 = COUNT_BIG(L.ListingCol3),
        CountCol4 = COUNT_BIG(L.ListingCol4),
        CountCol5 = COUNT_BIG(L.ListingCol5)
    FROM dbo.Listing AS L
) AS SC
CROSS APPLY 
(
    -- Median for column 3
    SELECT
        MedianCol3 = AVG(1.0 * SQ.ListingCol3)
    FROM
    (
        SELECT 
            L3.ListingCol3
        FROM dbo.Listing AS L3
        WHERE 
            L3.ListingCol3 IS NOT NULL
        ORDER BY 
            L3.ListingCol3 ASC
        OFFSET (SC.CountCol3 - 1) / 2 ROWS
        FETCH NEXT 1 + (1 - SC.CountCol3 % 2) ROWS ONLY
    ) AS SQ
) AS SQ3
CROSS APPLY 
(
    -- Median for column 4
    SELECT
        MedianCol4 = AVG(1.0 * SQ.ListingCol4)
    FROM
    (
        SELECT 
            L4.ListingCol4
        FROM dbo.Listing AS L4
        WHERE 
            L4.ListingCol4 IS NOT NULL
        ORDER BY 
            L4.ListingCol4 ASC
        OFFSET (SC.CountCol4 - 1) / 2 ROWS
        FETCH NEXT 1 + (1 - SC.CountCol4 % 2) ROWS ONLY
    ) AS SQ
) AS SQ4
CROSS APPLY 
(
    -- Median for column 5
    SELECT
        MedianCol5 = AVG(1.0 * SQ.ListingCol5)
    FROM
    (
        SELECT 
            L5.ListingCol5
        FROM dbo.Listing AS L5
        WHERE 
            L5.ListingCol5 IS NOT NULL
        ORDER BY 
            L5.ListingCol5 ASC
        OFFSET (SC.CountCol5 - 1) / 2 ROWS
        FETCH NEXT 1 + (1 - SC.CountCol5 % 2) ROWS ONLY
    ) AS SQ
) AS SQ5;

Expected execution plan shape: