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How to average the last 5 nonblank, nonzero value in a row in Google Sheets?

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I run a disc golf league and in order to track handicaps we take an average of the last 5 rounds played. I currently have the player name in column A, the handicap in B, # of rounds played in C, best round in D, then a manual average of the last 5 in E. then the next 33 columns are the weekly scores for each player.

I'm wondering if there is a formula that can capture the last 5 (or less) weeks scores and average them, accounting for the fact that not every player plays every week, so there are lots of blank cells.


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