1. **State the problem:** Find the coordinates of the centroid of triangle $\triangle PQR$ with vertices $P(-7,7)$, $Q(4,2)$, and $R(3,8)$.\n\n2. **Formula for centroid:** The centroid $G$ of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ is given by\n$$G\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$$\n\n3. **Apply the formula:** Substitute the coordinates of $P$, $Q$, and $R$:\n$$x_G = \frac{-7 + 4 + 3}{3} = \frac{0}{3} = 0$$\n$$y_G = \frac{7 + 2 + 8}{3} = \frac{17}{3} \approx 5.67$$\n\n4. **Interpretation:** The centroid is the average of the $x$-coordinates and the average of the $y$-coordinates of the vertices. It represents the center of mass of the triangle.\n\n**Final answer:** The coordinates of the centroid $G$ are $\boxed{\left(0, \frac{17}{3}\right)}$ or approximately $(0, 5.67)$.