If you count mountain masses, then it depends on how deep you go.
If you want to learn how the National Geodetic Service calculated it, here you go.
Believe it or not, in 1918 the National Geodetic Survey made a precisely cut cardboard cutout of the contiguous US (of uniform thickness), and found its balance point on a pin. That spot was 39°50′ N and longitude 98°35′ W, the closest town being Lebanon, KS.
One of my professors told us that the way he did numerical integrals was to graph the function on paper, cut it out, and weigh it on an analytical balance.
I used to use a bamboo Post for multplication, square roots and trig.
Huh? You graph it, okay, but you do not need to cut it out:
However, if you are starting from a table of numbers, why graph it?
If you cut it out of a thick enough piece, you can then locate the centroid by hanging the cutout from several different points, with a plumbline. The centroid will be where all the plumblines intersect.
Which even works for surfaces with voids or concavities. A little imprecise, but better than trying to support your hollow cutout by a pin in a “lake”.
Avulsion is like that. Rivers move abruptly but borders don’t. Leaving bits of state A on the state B side of the newly moved river.
There’s a famous bit of Iowa on the Nebraska side of the Missouri river just north of Omaha Nebraska’s Epply Airport.
I actually just learned, from a different thread here, that it’s not like that on the Rio Grande. By treaty, the US and Mexico actually exchange little pieces of land whenever the river changes course.
Given that it goes one way about as often as the other, and given that most of the land near the river isn’t worth much, that’s probably a sensible way to do it.
It is not north of the airport, it is west of it, and you can see the remains of the original oxbow as the crescent-shaped Carter Lake. That is a big chunk of land.
Saw a story today about a map of Africa used by the US State department that was breathtakingly incorrect, but it seemed improper to post it here. It is in a Pit thread.
I encountered the other day: If you go due south from Mexico, what South American country is the first one that you hit?
Peru, in the form of the Galapagos Islands. All of the continent of South America is east of the eastern border of Mexico.
A year ago I attended a Stanford graduation. For some reason, I thought Stanford was near LA, so I booked a flight to LAX. Thank God she immediately texted me to correct me! I was able to change the flight to San Francisco without a penalty or problem.
I think you mean Ecuador.
Yes, another one of my misconceptions. 
So you’re saying you deliberately made that error just to make your post appropriate to the thread topic?
Sure, let’s go with that.
I always have trouble recalling that most of South America is east of most of North America. It could very properly be called East America. I didn’t expect to have jet lag flying from Atlanta to Brazil.
It helps to notice a couple things. As shown on this zoomed out map:
The top edge of Mexico itself obviously starts under San Diego California and continues eastward to almost the middle of the US at Brownsville Texas. So it’s “holding up” the western ~50% of the USA. But as you proceed downwards into & through Mexico, the whole thing leans strongly to the right as it tapers into Central America.
Then Central America continues as a long tapering umbilical cord that slopes farther down and to the right from Mexico and finally plugs into the upper left corner of South America. Substantially all of South America is to the right of that plug-in.
Meaning South America is off to the right from Central America. Which is off to the right from Mexico. Which does start under the left half of the US, but more importantly, ends to the right of the Mississippi’s mouth in Louisiana.
That caricature of geography may be mnemonic for some of us.
A couple of my friends drove to Eureka, instead of Ukiah. oops.