@JBeaucaire:
if i get what the OP wants, i don't think that works because the the average you worked out in the source data is not based on the region. it does not change accordingly to the slicer. for eg. if i choose East in the slicer, i should get 180 because it would be the total time of 900 over just 5 records for Month 4. but yours would still be 189 because total time is still 3,400 over 18 records.
i think the PowerPivot would provide a solution, but i'm unfortunately not up for the job! let me just get OP on the route by activating it:
go to File tab -> Options -> Customize Ribbon -> on the right side, check the option of PowerPivot
convert data in sheet1 into a table. Select A1 & press CTRL + T
while A1 still selected, go to POWERPIVOT tab -> Add to Data Model
you will be brought to this PowerPivot window. Below the data are some cells where you can add something called Measures. This is where someone can hopefully help you with a formula. i am not sure if it's possible to refer to a value in the row labels though. it should go something like this (where i cant figure out the red portion to replace it to look at your month row labels)
AveTime:=CALCULATE(SUM(Table1[Time])/COUNTA(Table1[Time]),Table1[Day of month]<=1)
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