You should try to solve it with MySQL. Try something like this (replace 'your_scores_table' with your table name):
SELECT
Score.name,
AVG(Score.tscore) AS `avg`,
CONCAT(YEAR(Score.added), '-', MONTH(Score.added)) AS `year_month`
FROM
your_scores_table AS Score
GROUP BY
Score.name ASC,
YEAR(Score.added) DESC,
MONTH(Score.added) DESC
;