smc

To solve the problem, find the sum of the first $52$ terms of an arithmetic sequence with first term $2$ and common difference $1$ and divide that by $52$. The $52^{\text{nd}}$ term of the sequence is $2+51=53$, so the sum of the first $52$ terms of the sequence is $\frac{52(2+53)}{2}=1430$. Thus, the arithmetic mean is $\frac{1430}{52}=\frac{55}{2}=\boxed{27\frac{1}{2}}$.