Reputation histogram

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Generates a histogram of users' reputation. The histogram bins are automatically determined using Doane's formula, and the lowest bin is discarded since it would probably contain so many users that the rest of the histogram would be unreadable. Obviously best viewed as a graph.

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DECLARE @BinSize int;

-- After discarding users with < 150 reputation as outliers, calculate
-- an optimal number of histogram bins by applying Doane's Formula.
-- https://en.wikipedia.org/wiki/Histogram#Number_of_bins_and_width
WITH AvidUsers AS (
    SELECT Id
         , Reputation
        FROM Users
        WHERE Reputation >= 150
), Mean AS (
    SELECT AVG(Reputation) AS μ
        FROM AvidUsers
), Moments AS (
    SELECT COUNT(Id) AS n
         , μ
         , STDEV(Reputation) AS σ
         , AVG(POWER(CAST(Reputation - μ AS FLOAT), 4)) AS μ4
        FROM AvidUsers, Mean
        GROUP BY μ
), Kurtosis AS (
    SELECT n
         , μ4 / POWER(σ, 4) - 3 AS ɣ2
        FROM Moments
), DoanesFormula AS (
    SELECT CEILING(1 + LOG(n, EXP(1)) + LOG(1 + ɣ2 * SQRT(n / 6), EXP(1))) AS k
        FROM Kurtosis
), BinSize AS (
    SELECT ROUND(MAX(Reputation) / k, -2) AS BinSize
        FROM AvidUsers, DoanesFormula
        GROUP BY k
) SELECT @BinSize = BinSize FROM BinSize;


-- Be sure to plot the histogram bins with 0 members as well.
-- e3 is just some arbitrary table with 81 rows.
WITH e1(n) AS ( -- 3
   SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1
), e2(n) AS ( -- 9
   SELECT a.* FROM e1 AS a CROSS JOIN e1 AS b
), e3(n) AS ( -- 81
   SELECT a.* FROM e2 AS a CROSS JOIN e2 AS b
), Bins AS (
    SELECT @BinSize * (ROW_NUMBER() OVER (ORDER BY n) + 0.5) AS bin
        FROM e3
), UserCounts AS (
    SELECT (Reputation / @BinSize + 0.5) * @BinSize AS Reputation
         , COUNT(Id) AS Count
        FROM Users
        GROUP BY Reputation / @BinSize
)
SELECT Bins.bin AS Reputation
     , COALESCE(Count, 0) AS Count
    FROM Bins
        LEFT OUTER JOIN UserCounts
            ON Bins.bin = Reputation
    WHERE Bins.bin <= (SELECT MAX(Reputation) FROM UserCounts)
    ORDER BY Bins.bin;

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