Trying to update a table with a customer sales averaging column - Oracle SQL
In the UPDATE statement you do not calculate the AVG per customer but an AVG on all customers. Put the customer identification in the where clause. The GROUP BY option is not needed since the AVG column is the only column in the SELECT statement (see other reply by @_horse_with_no_name):

UPDATE t1
SET AVG_AMOUNT=(SELECT AVG(INVOICE_TOTAL)
                FROM   t1 a1
                where  t1.customer_ID = a1.customer_ID);