MySQL-MAX値のサブセットのAVGを計算する

1日の最大値の合計平均：

SELECT AVG(dailyMax) AS avgOfDailyMax
FROM (SELECT Date, MAX(Score) AS dailyMax FROM MyTable GROUP BY Date) as DailyMaxTable 

および毎日の最大値：

SELECT Date, MAX(Score) AS dailyMax
FROM MyTable
GROUP BY Date