It needs to be not only installed but enabled (under Tools/ Addins).
If that looks OK you could try disabling the Add-in, coming out of Excel (&
possibly rebooting your machine), then re-opening Excel and re-enabling the
Add-in. Excel does sometimes "forget" that the add-in was enabled.
Or going back to the last bit of your message, "Data Analysis" won't appear
on the Tools menu if you are looking at a chart, rather than a worksheet.
The menus for a chart are very different from the menus for a worksheet.
Data Analysis is a worksheet function, not a chart function. Go to a
worksheet, rather than a chart, and look again at your Tools menu.