There is no published memory-care cost median anywhere -- CareScout does not survey memory care as a separate category, in Ohio or any other state. Any specific price you find online is an estimate, not a surveyed figure.
The detail behind the number
This is one of the more frustrating gaps in publicly available senior care data, and we'd rather say so plainly than make up a number to satisfy a search query. Memory care pricing varies enormously by community, by the specific level of secured supervision required, and by staffing ratios that go well beyond standard assisted living. The only reliable way to get a real number is to ask each community directly for a written, all-in monthly quote at your parent's current assessed care level, and to ask for the community's rate-increase history over the last three years so you understand what that number is likely to become.