Obtain a 'flowing' average from blocks of data

Apologies for the novice terminology.
I have created the attached Excel spreadsheet which is a very simple representation of my real data set to help illustrate my query. It should be viewed in conjunction with the attached jpeg image for greater clarity.
I'm trying to establish what a more realistic individual daily average would be based on only knowing what the total of a set of multiple day periods is. The catch is I still need the sum of all the 'adjusted' averages in any given period to equal the known total for that period. Also these periods are not necessarily all the same number of days.
I'm aware this may seem to cross over into the charts area but I'm not actually using charts in my workbook. I'm a graphic designer and I created the attached chart manually just to help explain the results I'm trying to achieve.
The overall purpose of this is to help me analyse 4 years of electricity bills in detail to ascertain whether getting solar panels is worthwhile for us.

Please explain how you calculated the 1.8, 1.73 etc. in column E.