There are some easy things you can do to help, and some not so easy.
The first step is to throw that rug out, even if you love it, you great grama gave it to you.... you cat has marked it. This isn't always the case but is sure doesnt help. You might get away with washing the hell out of it, there are special soaps (if you wanna go that far)
Second step, get a fecal test done. These are normally cheep and vets will run em with out appointments(some can be stingy). I DOUBT this is the problem unless she is going there at least once a day.(this may or may not be nessasary)
Third step, get another box OR MORE! Some cats like one box for poo and one box for pee. Others like options or can be picky about litter. I would try to get another box with same litter and if you can put that box in the spot she was going. (remember with litter "less is more" normally cats don't like tons on litter)
That should do it... there are some materials on websites if you need more help, or just pm me.

quite smart, shits on floor
pick one

Actually il pick both,

Not cause she poop on the floor, that means shes not smart.


Im in no way comparing her to einsten but einsten did not start talking until he was 4 years old.
yet hes one of the smartest person to ever walked this earth.

Instead of changing the rug

Get rid of all the rugs

My cat was shittin all over like a crippled raccoon, we got one of those litter boxes with the cover on it, it looks like an igloo, now we're good to go

iv had many cats in my lifetime used to have 2 of them. if your cat is only doing this sometimes or consistently there is probably something wrong, if she is not pooping in litter box its because the first time she shit and was in pain it was there and she will associate the pain to the litter box.therefore she wont go there.