Recently, I have used Software Updater tool of Avast Free Antivirus 2015 to update the outdated software on my computer to the latest version. My question is whether this tool automatically deletes the downloaded files after finishing the installations. I find no such option in the settings of this tool.
If downloaded files are deleted or not depend on how the author of the software programmed their installer(s).
avast detects a version you have installed and compare it with the latest version released.
When there is a newer version and you select update, the installer for the latest version is downloaded and run.
If so, I have another question for you as follows: Which directory does Avast put the downloaded installer(s) in?
They are most likely put into a temp folder, run and discarded. (I could be wrong.)