You usually do not want to use FindFit with Erfc. Scientists try to do this all the time, but it's usually wrong.
If you need to find the parameters of a distribution, look at FindDistributionParameters. Look at what algorithms it uses.
http://reference.wolfram.com/language/ref/FindDistributionParameters.html
In summary, statistical curve fitting and estimating the parameters of a distribution are related tasks, but don't confuse them. There are methods for finding the parameters of different distributions. They exist for very important statistical reasons.
The technique you are using can give okay results with well behaved sets of data.
There are many different kinds of averages. Which is the correct one to use in your research? This is an important question.
Your code fails at this line:
ff1 = FindFit[f, model1, {a, \[Mu], \[Sigma]}, x]
The variable "f" is a Plot. The argument must be a list of data points. You need to create a list of data points.
In the plot, you do this using an Interpolation of each function and then averaging the Interpolations. How would you choose to do this for the data?
