I am working on a small proof/demonstration of how the least squares method gives us the arithmetic mean.

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In[1]:= X := {x1, x2, x3}

In[2]:= Err[mu_] := X - mu

In[3]:= SSE[mu_] := Total[Err[mu]^2]

In[4]:= SSE'[mu]

Out[4]= -2 (-mu + x1) - 2 (-mu + x2) - 2 (-mu + x3)

In[5]:= Solve[SSE'[mu] == 0, mu]

                x1 + x2 + x3
Out[5]= {{mu -> ------------}}
                     3

I would like a more general version where X has an arbitrary length, X := {x1, x2, x3, ... , xn}. Is there a way to express a vector of variable length? What I am ultimately looking for is mu -> (x1 + x2 + x3 + ... + xn) / n.