jmc

Since $1,2,3,\dots ,250$ is an arithmetic sequence, the mean of all of the terms is equal to the mean of the first and last terms. (To see this, remember that the sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms.) So the mean is $\frac{1}{2}(1+250)=\boxed{125.5}$.