Here is one way...(and there are surely others)

Beginning in A371 and down, put in the actual date (i.e., 1/1/16, 2/1/16, 3/1/16 etc)

Then in B371 copied down

=SUMPRODUCT(--(MONTH($A$3:$A$368)=MONTH(A371)),$B$3:$B$368)/SUMPRODUCT(--(MONTH($A$3:$A$368)=MONTH(A371)))

In A371, place a custom format to get January, February etc

Custom Format

• Right click cell (or Ctrl + 1)
• Format Cells
• Number
• Custom
• Type: mmmm