There is no published memory-care median anywhere in the country -- CareScout does not survey memory care as its own category, in Texas or any other state. Any specific memory-care dollar figure you see online is an estimate or an extrapolation, not a sourced statistic.
The detail behind the number
We could publish an estimated number here. It would probably get more search traffic than an honest non-answer does. We don't, because families make six-figure decisions off pages like this one, and a made-up number dressed up as data does real harm. What actually works: ask every community you tour for the all-in monthly cost at your parent's current assessed care level, in writing, along with what triggers a move to the next care level and what that costs. Ask for the rate increase history over the last three years too -- that tells you more about what you'll actually pay two years from now than any published average would.