I purchased a used computer. I am set up as the administrator but how do I delete the previous owner as administrator also and it still says his computer

The person that previously owned the Mac did not follow the steps in What to do before you sell, give away, or trade in your Mac

. Thus, the operating system that is on it, and any installed applications are still tied to the previous owners Apple ID, and your just taking over the Mac will cause you grief until you perform a clean installation of macOS, and associate the machine with your Apple ID. Just removing their user account isn't the solution that is needed.

Since you did not provide the Mac (introduction date) from the menu : About This Mac, I don't know which version of the operating system originally came with the Mac, or what it can be upgraded too. Provided this is a machine manufactured after Summer 2011, you may want to perform an Internet Recovery of the operating system that originally shipped on it, providing your own unique Apple ID and user account, then upgrade from there to the lastest operating system supported by this Mac model.

Do as @VikingOSX suggested and perform a clean install of macOS by first erasing the whole physical drive before reinstalling macOS. Since you can use the system I highly recommend downloading macOS 10.11 El Capitan (or a more recent version of macOS if supported) and create a bootable macOS USB installer using these instructions:

https://support.apple.com/en-us/HT201372

I would never trust an OS on a computer I've received from someone else (even if I know the person). You never know what might be installed which will cause you problems down the road. You should always wipe out the drive and perform a clean install. You are just asking for trouble if you don't. Being unable to delete a user account is just the first of the issues from not performing a clean install. Consider that there may be some very subtle issues that you haven't even noticed yet.

You should not need to install an intermediate OS if the computer was previously running High Sierra. The only reason to install 10.11 first is if you cannot access the High Sierra installer in the App Store.

Since Lion is so old Safari and most other browsers won't work unless you can find one which someone has made a current browser to work with 10.7.

If the computer was previously running High Sierra, then you should be able to boot into Internet Recovery Mode using Command + Option + R to boot the online version of the macOS installer. Using this key combination will access the highest compatible version of macOS for this computer.

To remove the other user:

• Log in as you.
• Go to System Preferences > Users & Groups > (padlock) > (select the other user name) > (Click the music (-) button)

If the '-' is not available, you probably haven't hit the padlock icon to unlock it.

Sounds like you did! :)