on my ipod classic 160, itunes "summary" does not list the option to back up to my pc

The only way to get media onto the Classic is via iTunes, so there is nothing on an iPod Classic to back up. Your iTunes Library already serves as your backup. That's why you don't see a specific backup option.

What are you trying to achieve?

The backup option only applies to iOS devices. It doesn't include media that wasn't purchased from the iTunes Store. See Recover media from an iPod - Apple Community to reclaim any media that is only on your classic.

tt2