The reason it doesn't list a size is that it's a "plugin" (not an application) and due to the data storage requirements necessary to "stream" videos, the size can vary. So it lists as installed only.
Unless you're seeing messages that you need to update, or Flash content is otherwise NOT working... it's installed.
Many Thanks Mike. Further exploration shows I have the Active X version but the plugin version is not installed.
Download the following files by right clicking and selecting "Save target as".
Save ALL files to your Downloads folder - DO NOT RUN anything yet.
Reboot your system.
BEFORE opening anything else, go to your Downloads folder and run the UNINSTALLER first, and then the ActiveX Installer.
Once everything is installed, see:Enabling Flash Player in Internet Explorer to make 100% sure that Flash Player is enabled.