Short answer is yes you would have to sand the whole floor.

When was the last time it was refinished?
Can you get some pictures of said stain?
Is the stain in the center of room?

Thanks gregmills; the stain is not in the middle of the floor but closer to the wall. Will try to get a picture and download it to this message. We bought the house 3 yrs ago and the house was built in the late 1800's, so I have no idea when the floor was last refinished. Paul

Okay well chances are the floors were refinished after 1800 but probably not for a few years which means spot sanding the stain out and trying to blend the color to the rest if the floor will be difficult.
It can be done but to just spot sand and not refinish everything means you may have to deal with imperfections with blending color.

You still have options. Depending on color of you current floor the color may be pretty easy to match which means you could sand the stain out. Stain to match the floor add a couple of coats of finish and then recoat the entire floor to ensure a clean smooth transition. But this is dependant on the floor currently having a polyurethane finish and not a varnish or wax finish.

Fyi recoating the entire floor doesnt mean sanding everything to bare wood. Its simply abrading the top layer to allow the fresh coat to adhere.

Much cheaper to buff n coat (as its called) then to sand and refinish.
But this still is only an option ifvthe floors are currently finished with a polyurethane finish.