Weighted average based on dates selected in data range control

I am looking for a way to calculate the weighted average (based on the nr of people for a given score) in a scorecard for a given data range. See sample data and sample report below.

Sample data

https://docs.google.com/spreadsheets/d/1z3C4SOitKz7gJw80km3b8U3_YRtyPclL54d_teZvrVY/edit?usp=sharing

Sample report

https://lookerstudio.google.com/reporting/f08a5c6a-76cd-431b-9221-25513bf49ef4 

Conceptually I would like to create a calculated field SUM(score x people count) / total people count. 

What I tried so far ...

First select a data range that has some result. Based on the data I can get the normal average. I can also calculate the relative contribution to the whole based on people count. Looker is aware of the sum of all people count in the selected data range, I however cannot seem to use such a dynamic sum in a formula. 

Any suggestions would be much appreciated.

Cheers, Alard

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