Formal:
* Incorrectly
* Flawed
* Mistakenly
* Inaccurately
* Falsely
* Improperly
* Faultily
* Wrongfully
* Erratically
Informal:
* Wrong
* By mistake
* In error
* Off base
* Misguided
The best synonym will depend on the context and the specific nuance you want to convey.