[Svexav]

You would be wrong.

Make the problem simpler by thinking in 2 dimensions. Where's the center of the United States? There are an infinite number of different answers. Think about how many different map projections there are.

Now where is the center of the Earth? The point furthest from sea level? The point furthest from the surface? Do you include mountains, ocean basins, ocean trenches, etc.? What % of a substance has to be water before it doesn't count as part of the earth? The point furthest from the edge of the atmosphere? How do you determine where that is? Or is the center of mass? These are all going to give you wildly different answers.

Humanities questions cannot be easily solved scientifically.

[dikei]

The variation cause by mountain or sea trench is absolutely tiny compared to the earth diameter, as explained by his xkcd's link.