Get the Month of a week range based on which month has more dates in Data/Looker Studio

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How can I achieve this in Looker Studio's calculated field?

For instance, if my date range spans from October 30 to November 05, with the week beginning (WB) date set as October 30 (as it is a Monday), it should yield the result "November."

This outcome is desired because, among the dates in the given week (Oct 30 to Nov 05), there are only two dates (Oct 30 and 31) that fall within October, while the remaining dates belong to November.

In summary, the result should reflect the dominant month if the week's date range contains more dates pertaining to one particular month.

Date WB Monday Result
Oct 30, 2023 November
Nov 06, 2023 November
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