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The Center of Population: Definition & Significance

Instructor: Christopher Muscato

Chris has a master's degree in history and teaches at the University of Northern Colorado.

Where is the center of your population? This may be a more important question than you realize. In this lesson, we'll look at three ways to determine this and see why each is useful.

The Center of Population

Imagine that you wanted to start a transportation company. Your company's job would be to deliver products all around the country, and in order to make your company as efficient as possible, you decide to place your headquarters in the exact center of the country. This is the most efficient way to organize the flow of people, goods, and products from coast to coast.

As it turns out, you're not alone in this thinking. Many countries place their national capitals in the middle of the country for the same reason. Being centralized is more efficient. There's only one question: How do you determine the center point?

In establishing a shipping company, (or even a capital city), it's not the geographic center of the country that matters as much as the center of population, or the point at which you are in the middle of the population. This gives you to most efficient access to the greatest number of people. But even this can mean different things. It all depends on how you define the center.

The Geometric Median

There are three major ways to calculate the center of a population, each of which will give you different results. Let's start with the geometric median. This measurement will pinpoint the place with the point of minimum aggregate travel. In essence, you're looking for the point with the lowest average travel distance for all people in the country.

So, what's that mean? Imagine a completely flat map of the USA, which doesn't consider mountains or anything like that. Now place a pin in it somewhere. Imagine that you could draw a straight line from every person's home to that point, measure the distance of each line, and then calculate the average. That would be the average distance of travel. We're looking for the point where that number is smallest, representing the minimum distance of average travel. Recently, the California Polytechnic State University math department determined that the geometric median of the United States was in Greene County, Indiana, with the average distance of travel being 795 miles between any person and this point.

Estimated geometric median of the United States
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The Median Center

Geometric median is one way to find the center of population, but it isn't the only one, nor is it necessarily the most reliable. Another way to calculate this is to look for the median center, which is the numerical middle point. Geometric median looks at the average distance between people, but median center looks for the actual middle, regardless of distance.

The median is calculated by two different formulas. The first examines the distribution of people and finds the longitudinal center. Basically, the question is this: Where would you have to draw a line down the country so that exactly half was to the east of that line, and half was to the west? The second half of the equation, of course, is to find the line of latitude that divides the population between north and south. The median center is the point where these lines meet. Numerically, that's the center of the population. In the United States, the US Census Bureau calculated this point to be in Clay Township, Pike County of Indiana as of 2010.

Estimated median center of the United States
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The Mean Center

The final measure of center of population, and the one most used by the United States government's Census Bureau is the mean center. The mean center is the point of population balance. So, what's that mean?

Imagine the United States as a completely flat board. For every person in the USA, place an equal weight of exactly 1 ounce on the board, in the location of their home. Now place the US-shaped board, (with its 323 million individual weights), on the tip of a vertical pole. If every individual is represented by the same weight, the mean center is the point where these weights are balanced. For the United States, that point is in Missouri, 2.7 miles northeast of the village of Plato, in Texas County, according to the US Census Bureau. If you placed the US-shaped board on the pole at this point, the board would balance and not tip over.

Estimated mean center of population of the United States
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