The center of population is somewhere near the center of the Earth. The standard map with Europe in the middle is just an historical influence too!
Usually people just use the surface of the earth for this.
The funny thing is calculating it at high resolution would require classified data (the best measures of the exact shape of the earth are classified; they are used in ICBM flight path calculations, and deviation from an oblate spheroid is significant when you want to put something on a tennis court from the other side of the world. The exact distribution of mass (some concentrations of heavier materials) and magnetism (for MAD detection of submarines) are similar.
Center of population is somewhere near Afghanistan I think, but that's kind of a silly measure (like "the average person is 50% male").
US manufacturing production was #1 from 1895-2010. China is #1 now, but the US numbers are far more certain than China. If you look at total industrial base, the US is far above China (wealth vs. income, basically). I think Japan and a bunch of European nations actually would beat China on that metric.