SELECT
    a.*,
    lead(avgv,-1) over (partition by "MONTH" order by "DOY") as prev,
    a.avgv-lead(avgv,-1) over (partition by "MONTH" order by "DOY") AS prev_avg_diff,
    b.median
FROM (
      SELECT
         EXTRACT(YEAR FROM "created_on") AS year,
         EXTRACT(mon FROM "created_on") AS month,
         EXTRACT(dayofyear FROM "created_on") AS doy,
         COUNT(*) AS cnt,
         AVG("value") AS avgv
      FROM mydata4
      GROUP BY
         EXTRACT(YEAR FROM "created_on"),
         EXTRACT(mon FROM "created_on"),
         EXTRACT(dayofyear FROM "created_on")
      ORDER BY
         EXTRACT(YEAR FROM "created_on"),
         EXTRACT(mon FROM "created_on"),
         EXTRACT(dayofyear FROM "created_on")
     ) a
LEFT JOIN (
          SELECT
            tmp.year2,tmp.month2,
            MEDIAN(tmp.cnt) AS median
          FROM (
                SELECT
                  EXTRACT(YEAR FROM "created_on") AS year2,
                  EXTRACT(mon FROM "created_on") AS month2,
                  EXTRACT(dayofyear FROM "created_on") AS doy2,
                  COUNT(*) AS cnt
                FROM mydata4
                GROUP BY 1,2,3
            ) tmp
            GROUP BY 1,2
          ) b ON b.month2 = a.month AND b.year2 = a.year
WHERE a.cnt > b.median ;