How to select MAX from AVG?

I’m practicing for my SQL exam and I can’t figure out the following question:

“Of the average amount paid per customer, show the highest amount.”

So to retrieve the average amount paid, I would do the following:

SELECT AVG(Amount) AS 'Average amount paid'
FROM Payment;

Then I would like to retrieve the highest average amount out of this list of averages. I thought the following would do the trick:

SELECT MAX(AVG(Amount)) AS 'Highest average amount paid'
FROM Payment;

This doesn’t seem to work. I get the following error:

Cannot perform an aggregate function on an expression containing an aggregate or a subquery.

I would like some help with this. What is the correct way to approach this? Thank you in advance.

Answer

In SQL Server, you can order the records and use TOP 1 to keep only the record that has the highest amount:

SELECT TOP 1 Customer_id, AVG(Amount) AS [Average amount paid]
FROM Payment
GROUP BY customer_id
ORDER BY [Average amount paid] DESC;

Note: for this query to make sense, you need a GROUP BY clause. Without it, it would just return one record, with the average of payments within the whole table.