So after "letting them negotiate you down" -- what's the actual, final, median rate we're talking about here, please?

I would say $180-$200.

I would agree with this. I have a number of friends doing Data Science consulting (PowerBI/Tableau/etc), and it seems like they average out around the $180-200 range. I think they're undercharging, and I've had no problems getting business/repeat business up to around $250. Beyond that and you're in the bailiwick of the Accentures and their ilk.

The more projects you do, the more repeat business, the better you get, and the more you learn to not underprice you work (which helps you focus on the good projects where you can have the most impact). It pretty much compounds.

For the hourly stuff, I've had very little pushback until I get much above $250. Most of that work is break/fix. As above, I much prefer to do project based work and bid on a project by project basis. (Gives me incentive to work harder/faster, and gives the customers a predictable price. I've found a lot of them are wary of open-top ended contracts).

What's your effective day rate using on an average project based price if you don't mind sharing?

Ooo. Good question. I will admit I haven't run the numbers recently. Will do so and post.

Noted, thanks.

I stand by the range. There are certainly gigs where you can charge more, and it's undoubtedly also location dependent. But those are on the edges of the bell curve. Most people in the field will encounter rates comparable to what I've described.