How can I replace certain values by their average in an sqlite database?

I have an sqlite database with a table that logs electric power values over time, i.e. there is a timestamp column and one for the associated power value.

With a value coming in roughly every second, this table grows significantly over time. Which is why I want to thin out old values, for example by replacing all 60 values in a minute with their average.

I know how to query for the average. I know how to insert the query's result back into the table. But how do I delete the original values without also deleting the newly inserted average value (which has a timestamp within the same range)?

Note that I would like to perform the operation entirely inside sqlite query language, i.e. without storing for example row ids in the C code that is executing the queries.