Centroid of Population in Plato, MO

NOAA:

If you filled out the 2010 Census form from the U.S. Census Bureau, then you had a part in defining the centroid — the point where the center of the U.S. population falls. Every 10 years, after the Census Bureau crunches the numbers and figures out where the centroid is, NOAA’s National Geodetic Survey (NGS) places a geodetic survey disk (also called a survey marker, monument, or bench mark) in the incorporated community closest to its exact geographic location.
NOAA Chief Geodetic Surveyor Dave Doyle, who has helped place a survey marker at the centroid every 10 years since 1980, says first to think of a rectangular-shaped state like Colorado. “If you imagine Colorado as a perfectly flat plain without all the mountains and valleys, and you put it on a map, the place where this rectangular shape balances perfectly on a point is the centroid.”
“Then, think of the United States, including Alaska and the territories, as a flat plain and put it on a map. Imagine also that every individual in the population weighs exactly the same,” he continues. “The centroid is where the center of the population is located.”
The process that the Census Bureau uses to figure out the centroid for the U.S. population is more complicated, but that’s the basic idea.