The USCIS publishes processing times for the N-400 Application for Naturalization Form (mirror).
Processing time is the number of months that elapse between the date we receive an application, petition, or request and the date we complete the application, petition, or request (that is, when we approved or denied it) for all cases for a specific form for the latest completed 6 months.
When is an N400 considered approved or denied when the USCIS computes the processing time? Is it when the letter notifying the interview appointment is sent? When the interview takes place? When the oath takes place? Some other time?