Say for example it's a two month iOS development project, would it be sensible to set the fixed cost at what two months of a mobile developers salary in the U.S. would be using this data? I'm in the SF Bay Area. I want to avoid low-balling myself while also making what I charge more objective and backed by data. This would be the only project and client I work on during this period.
Your situation as a freelancer typically places additional burdens upon you that aren't reflected in that salary survey, which is primarily geared toward people seeking employment.
Very often, billing rates for a professional are the professionals' salary plus some sort of multiplier. The multiplier varies a lot depending on the industry, but it's purpose is to cover the costs of things like overhead.
Overhead, in a general sense, are costs like office space (even if that's a room in your house), utilities, software license fees, hardware, expenses for marketing, health insurance, taxes, etc. Effectively, anything and everything that's necessary to do the work. For a company, it would also include things like profit. Presumably as a freelancer your salary is the profit; however, if you're thinking to expand your freelancing into some sort of business, then you should also include profit.
In my industry of consulting engineering, we have a lot of overhead costs and I've seen multipliers as high as 3.2. So if my salary is $35 per hour the client's getting billed at least $112 per hour.
As a freelancer, you can probably curb a lot of the costs and bring that multiplier down a bit (perhaps a lot). If you haven't done a rough cost analysis on your overhead costs, it's going to really hamper your ability to determine an appropriate multiplier since you're just guessing at that point.
So as the developer Survey states the average salary of an iOS developer, you definitely need to charge little more. Let's suppose a developer earns 100% for a two-month job, so you need to charge 120%-140% of it. A freelancer always charges more than a full-time developer, as you might be giving more time than a full-time developer or you possess more experience than an average developer.
Secondly, once the task is complete, the client will be asking for revisions too that might take the duration to more than two months. So you need to keep this into consideration too.
I hope it helps. Feel free to ask if you still have any queries...