Average of a function and center of mass

Question

The geometric center of an object is the center of mass of an object with uniform density. The average height of a semicircular wire is $\pi R/4$ where R is the radius. But the actual y coordinate of the center of mass is $2R/\pi$ why is it different? someone help. I calculated the average height by using the standard formula, $$\frac{1}{2r}\int_{-r}^r \sqrt{r^2-x^2} \,dx= \frac{\pi R}{4}$$. and the second result was by using the standard substitu