You can tweak the map to be map { "avg($_) as $_\n" } to make it a little more legible, and then browse for errors. Did you try running the SQL directly in your db? What about a portion (e.g. w/just a few columns) of it?
If you want to exclude columns, simply grep them out of @cols, or to just ditch the first one, do a shift @cols;
Doing all the average calculations in one command may be a little taxing on my system.
No, doing all the average calculations in many commands is what will tax your system. If you do it in separate statements, you're making the database go through all 6000 rows 30 different times. But if you do it in one statement, it only needs one pass.
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