Your two ways does't make a difference, they give the same result. You can use algebra to check that $$ \frac{x_1+\dotsm+x_n+\bar{x}}{n+1}=\bar{x} $$ where $\bar{x}\frac{x_1+\dotsm+x_n}{n}$ is the mean.

Your two ways are not different: they give the same result. You can use algebra to check that $$ \frac{x_1+\dotsm+x_n+\bar{x}}{n+1}=\bar{x} $$ where $\bar{x} = \frac{x_1+\dotsm+x_n}{n}$ is the mean.