In order to have the highest median value, the average of the 6 and 7 month, you have to make it such that the first 5 months are at a minimum(0.2) so as to keep the most for the median value when you reach 6th and 7th month.

For the values above the 7th month, you have to minimize them so as to keep, save, the highest possible score for the 7th month. However, you know that the highest month is 12.2 so get that one out of the way as I did and you will have the remainder (28.8) which you can now spread over the remaining 6 middle months (6,7,8,9,10,11). This way, you will maximize the median which is b/w 6th and 7th month

From lowest to highest raining month:

1: 0.2

2: 0.2

3: 0.2

4: 0.2

5: 0.2

6: 4.8

7: 4.8
8: 4.8

9: 4.8

10: 4.8

11: 4.8

12: 12.2

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Best Regards,

Paul