Pro rata data over previous days

OK, this is mainly about cleaning up your data. I created an Enter Data query and put in your information minus the "." and I did it in two columns, with the "Units Used" in a column and the rest in another column. Then I used the transformation functions in the query editor to split it all out like so:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMiwuUfBNrFQoyVcwNCrJALGVdJTMTA2UYnWAssYQIbC0OVza2AAqbYGQNspLUfAqzUsFShsagORjAQ==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [#"Reading Start Date" = _t, #"Units Used" = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Reading Start Date", type text}, {"Units Used", Int64.Type}}),
    #"Split Column by Delimiter" = Table.SplitColumn(#"Changed Type","Reading Start Date",Splitter.SplitTextByDelimiter(" to ", QuoteStyle.Csv),{"Reading Start Date.1", "Reading Start Date.2"}),
    #"Changed Type1" = Table.TransformColumnTypes(#"Split Column by Delimiter",{{"Reading Start Date.1", type text}, {"Reading Start Date.2", type text}}),
    #"Renamed Columns" = Table.RenameColumns(#"Changed Type1",{{"Reading Start Date.1", "Reading Start Date"}, {"Reading Start Date.2", "Reading End Date"}}),
    #"Split Column by Delimiter1" = Table.SplitColumn(#"Renamed Columns","Reading Start Date",Splitter.SplitTextByDelimiter(" ", QuoteStyle.Csv),{"Reading Start Date.1", "Reading Start Date.2"}),
    #"Changed Type2" = Table.TransformColumnTypes(#"Split Column by Delimiter1",{{"Reading Start Date.1", type text}, {"Reading Start Date.2", type text}}),
    #"Split Column by Delimiter2" = Table.SplitColumn(#"Changed Type2","Reading End Date",Splitter.SplitTextByDelimiter(" ", QuoteStyle.Csv),{"Reading End Date.1", "Reading End Date.2"}),
    #"Changed Type3" = Table.TransformColumnTypes(#"Split Column by Delimiter2",{{"Reading End Date.1", type text}, {"Reading End Date.2", type text}}),
    #"Renamed Columns1" = Table.RenameColumns(#"Changed Type3",{{"Reading Start Date.1", "Reading Start Day"}, {"Reading Start Date.2", "Reading Start Month"}, {"Reading End Date.1", "Reading End Date Day"}, {"Reading End Date.2", "Reading End Date Month"}}),
    #"Replaced Value" = Table.ReplaceValue(#"Renamed Columns1","st","",Replacer.ReplaceText,{"Reading Start Day"}),
    #"Replaced Value1" = Table.ReplaceValue(#"Replaced Value","nd","",Replacer.ReplaceText,{"Reading Start Day"}),
    #"Replaced Value2" = Table.ReplaceValue(#"Replaced Value1","rd","",Replacer.ReplaceText,{"Reading Start Day"}),
    #"Replaced Value3" = Table.ReplaceValue(#"Replaced Value2","th","",Replacer.ReplaceText,{"Reading Start Day"}),
    #"Replaced Value4" = Table.ReplaceValue(#"Replaced Value3","st","",Replacer.ReplaceText,{"Reading End Date Day"}),
    #"Replaced Value5" = Table.ReplaceValue(#"Replaced Value4","nd","",Replacer.ReplaceText,{"Reading End Date Day"}),
    #"Replaced Value6" = Table.ReplaceValue(#"Replaced Value5","rd","",Replacer.ReplaceText,{"Reading End Date Day"}),
    #"Replaced Value7" = Table.ReplaceValue(#"Replaced Value6","th","",Replacer.ReplaceText,{"Reading End Date Day"})
in
    #"Replaced Value7"

Then I created a custom column in DAX that is simply "2016" like:

Year = 2016

Now you need a Month table (Enter Data query) like:

Reading End Month Num = RELATED(MonthsEnd[MonthNum])

Month	MonthNum
January	1
February	2
March	3
April	4
May	5
June	6

I actually created 2, MonthsStart and MonthsEnd

Relate your Reading Start Month and Reading End Month columns to the MonthsStart and MonthsEnd columns respectively.

2 more custom columns:

Reading Start Month Num = RELATED(MonthsStart[MonthNum])

And 2 more custom column:

StartDate = DATEVALUE([Reading Start Month Num] & "/" & [Reading Start Day] & "/" & [Year])

EndDate = DATEVALUE([Reading End Month Num] & "/" & [Reading End Date Day] & "/" & [Year])

Now the final two columns:

DaysBetween = DATEDIFF([StartDate],[EndDate],DAY)

Average = [Units Used]/[DaysBetween]

This is by no means elegant, but then again, neither is your source data. :) Basically, I just hacked this together to give you the general gist of what you need to do and a vehicle to get there, there are much better approaches I am sure.