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This probably has a straightforward answer that I'm too tired to figure out right now, but here goes.

Clark County, Nevada -- my home county -- contains the vast majority (almost three-quarters) of the state's residents. For those who may not be aware, and as the map in the Wikipedia article shows, it is located in the southernmost tip of the state. It also extends further east than any other county in Nevada and is approximately tied for being the county with the easternmost geographic center in the state.

Based on this, if there is a parallel of latitude such that half of Nevadans live north of it and the other half south of it, it is bound to pass through Clark County. Similarly, a meridian of longitude with half of Nevadans east of it and half west of it will also pass through Clark County. Thus, assuming the county borders don't become concave at any point that we care about (note that the border does go concave in the southeast, at the Arizona state line, but this is not the side we're concerned about -- see below), the intersection of this parallel and this meridian must be in Clark County, and thus there must be some point in Clark County that has equal amounts of Nevada population "mass" on each side of it (well, when considering the north-south and east-west axes, anyway).

Despite this, however, Wikipedia, as well as several other sources that I've looked at, state that Nevada's center of population is in Nye County. Specifically, it is close to Yucca Mountain, which is located both entirely north and entirely west of Clark County.

Where does the discrepancy lie here? How can the center of population not be in the county that contains 75% of the residents? Am I misinterpreting the definition of center of population? Is my approach of considering the balance only in the north-south and east-west directions incorrect (i.e., could the center of population be different if I did the "halving" with northwest-southeast and northeast-southwest lines instead)?

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  • $\begingroup$ If most of the population of each of the four quadrants is in the upper left corner of the quadrant, the center of population could be outside the populous southeastern quadrant. $\endgroup$ – Gerry Myerson Jul 30 '16 at 6:06
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    $\begingroup$ The mean of a set of data can be strongly influenced by outliers. $\endgroup$ – Aweygan Jul 30 '16 at 6:07
  • $\begingroup$ Consider a simpler example in one dimension. If you have 99 people clumped at the point $0$, and you have one far away person at the point $10000$ then the center of mass will be at the point $100$, which is not "near" the clump of people at $0$. So, the center of population doesn't have to be near the huge population centers, especially in large states. $\endgroup$ – shalop Jul 30 '16 at 6:10
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    $\begingroup$ In particular, it's probably the population of Reno that's pulling the center of population off toward the northwest. $\endgroup$ – Gerry Myerson Jul 30 '16 at 6:10
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    $\begingroup$ Ah, my (and presumably Wikipedia's) definition of 'center of population' was that of "arithmetic mean" whereas the one you are assuming appears to be more of a "median" of coordinates. In either case, the center doesn't necessarily have to go through the largest city. $\endgroup$ – shalop Jul 30 '16 at 6:18
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https://en.wikipedia.org/wiki/Center_of_population There are multiple definitions. It is possible for the center of population not to be in a very populated place if they use a mean center. Think of trying to balance 2 weights on a board, one far heavier than the other.

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