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Congress, each state is represented in the Senate irrespective of population size by two senators, and each is guaranteed at least one representative in the House.

Both senators and representatives are chosen in direct popular elections in the various states. Prior to , senators were elected by state legislatures.

There are presently senators, who are elected at-large to staggered terms of six years, with one-third of them being chosen every two years.

Representatives are elected at-large or from single-member districts to terms of two years not staggered. The size of the House—presently voting members—is set by federal statute.

Seats in the House are distributed among the states in proportion to the most recent constitutionally mandated decennial census.

Citizens in each state plus those in the District of Columbia indirectly elect the president and vice president. When casting ballots in presidential elections they are voting for presidential electors , who then, using procedures provided in the 12th amendment , elect the president and vice president.

While the Constitution does set parameters for the election of federal officials, state law, not federal, regulates most aspects of elections in the U.

All elections—federal, state and local—are administered by the individual states, and some voting rules and procedures may differ among them.

Article V of the Constitution accords states a key role in the process of amending the U. Amendments may be proposed either by Congress with a two-thirds vote in both the House and the Senate, or by a convention of states called for by two-thirds of the state legislatures.

Article IV also grants to Congress the authority to admit new states into the Union. Each new state has been admitted on an equal footing with the existing states.

This caveat was designed to give Eastern states that still had Western land claims including Georgia, North Carolina, and Virginia , to have a veto over whether their western counties could become states, [19] and has served this same function since, whenever a proposal to partition an existing state or states in order that a region within might either join another state or to create a new state has come before Congress.

Most of the states admitted to the Union after the original 13 were formed from an organized territory established and governed by Congress in accord with its plenary power under Article IV, Section 3, Clause 2.

In some cases, an entire territory has become a state; in others some part of a territory has. When the people of a territory make their desire for statehood known to the federal government, Congress may pass an enabling act authorizing the people of that territory to organize a constitutional convention to write a state constitution as a step towards admission to the Union.

Each act details the mechanism by which the territory will be admitted as a state following ratification of their constitution and election of state officers.

Although the use of an enabling act is a traditional historic practice, a number of territories have drafted constitutions for submission to Congress absent an enabling act and were subsequently admitted.

Upon acceptance of that constitution, and upon meeting any additional Congressional stipulations, Congress has always admitted that territory as a state.

In addition to the original 13, six subsequent states were never an organized territory of the federal government, or part of one, before being admitted to the Union.

Three were set off from an already existing state, two entered the Union after having been sovereign states , and one was established from unorganized territory:.

Congress is under no obligation to admit states, even in those areas whose population expresses a desire for statehood. It existed for slightly over two years and was never approved by the United States Congress.

In another, leaders of the Five Civilized Tribes Cherokee, Chickasaw, Choctaw, Creek, and Seminole in Indian Territory proposed to establish the state of Sequoyah in , as a means to retain control of their lands.

Instead, the Indian Territory, along with Oklahoma Territory were both incorporated into the new state of Oklahoma in The first instance occurred while the nation still operated under the Articles of Confederation.

The territory comprising Franklin later became part of the Southwest Territory, and ultimately the state of Tennessee.

Additionally, the entry of several states into the Union was delayed due to distinctive complicating factors.

Among them, Michigan Territory , which petitioned Congress for statehood in , was not admitted to the Union until , due to a boundary dispute with the adjoining state of Ohio.

The Republic of Texas requested annexation to the United States in , but fears about potential conflict with Mexico delayed the admission of Texas for nine years.

As with any non-state territory of the United States, its residents do not have voting representation in the federal government. Puerto Rico has limited representation in Congress in the form of a Resident Commissioner , a delegate with limited voting rights in the Committee of the Whole House on the State of the Union , and no voting rights otherwise.

A non-binding referendum on statehood, independence, or a new option for an associated territory different from the current status was held on November 6, On December 11, , the Legislative Assembly of Puerto Rico enacted a concurrent resolution requesting the President and the Congress of the United States to respond to the referendum of the people of Puerto Rico, held on November 6, , to end its current form of territorial status and to begin the process to admit Puerto Rico as a State.

On June 27, , the H. House with the purpose of respond to, and comply with, the democratic will of the United States citizens residing in Puerto Rico as expressed in the plebiscites held on November 6, , and June 11, , by setting forth the terms for the admission of the territory of Puerto Rico as a State of the Union.

The intention of the Founding Fathers was that the United States capital should be at a neutral site, not giving favor to any existing state; as a result, the District of Columbia was created in to serve as the seat of government.

As it is not a state, the district does not have representation in the Senate and has a non-voting delegate in the House; neither does it have a sovereign elected government.

Additionally, prior to ratification of the 23rd Amendment in , district citizens did not get the right to vote in Presidential elections.

Some residents of the District support statehood of some form for that jurisdiction — either statehood for the whole district or for the inhabited part, with the remainder remaining under federal jurisdiction.

In November , Washington, D. Other possible new states are Guam and the U. Virgin Islands , both of which are unincorporated organized territories of the United States.

Also, either the Northern Mariana Islands or American Samoa , an unorganized, unincorporated territory, could seek statehood. The Constitution is silent on the issue of whether a state can withdraw from the Union.

However, its predecessor document, the Articles of Confederation , stated that the United States "shall be perpetual.

In and , 11 southern states each declared secession from the United States, and joined together to form the Confederate States of America CSA.

Following the defeat of Confederate forces by Union armies in , those states were brought back into the Union during the ensuing Reconstruction Era.

The federal government never recognized the sovereignty of the CSA, or the validity of the ordinances of secession adopted by the seceding states.

White , held that states did not have the right to secede and that any act of secession was legally void.

Drawing on the Preamble to the Constitution , which states that the Constitution was intended to "form a more perfect union" and speaks of the people of the United States in effect as a single body politic, as well as the language of the Articles of Confederation, the Supreme Court maintained that states did not have a right to secede.

Four states — Kentucky, Massachusetts, Pennsylvania, and Virginia — adopted constitutions early in their post-colonial existence identifying themselves as commonwealths , rather than states.

These commonwealths are states, but legally, each is a commonwealth because the term is contained in its constitution. Virginia became a royal colony again in , and the word was dropped from the full title.

When Virginia adopted its first constitution on June 29, , it was reintroduced. This designation does have a legal status different from that of the 50 states.

Both of these commonwealths are unincorporated territories of the United States. The 50 states have taken their names from a wide variety of languages.

Twenty-four state names originate from Native American languages. Of these, eight are from Algonquian languages , seven are from Siouan languages , three are from Iroquoian languages , one is from Uto-Aztecan languages and five others are from other indigenous languages.

Of the remaining names, 22 are from European languages: Eleven states are named after individual people , including seven named for royalty and one named after a President of the United States.

The origins of six state names are unknown or disputed. Several of the states that derive their names from corrupted names used for Native peoples , have retained the plural ending of "s".

The borders of the 13 original states were largely determined by colonial charters. Their western boundaries were subsequently modified as the states ceded their western land claims to the Federal government during the s and s.

Many state borders beyond those of the original 13 were set by Congress as it created territories, divided them, and over time, created states within them.

Territorial and new state lines often followed various geographic features such as rivers or mountain range peaks , and were influenced by settlement or transportation patterns.

At various times, national borders with territories formerly controlled by other countries British North America , New France , New Spain including Spanish Florida , and Russian America became institutionalized as the borders of U.

In the West, relatively arbitrary straight lines following latitude and longitude often prevail, due to the sparseness of settlement west of the Mississippi River.

Once established, most state borders have, with few exceptions, been generally stable. Only two states, Missouri Platte Purchase and Nevada, grew appreciably after statehood.

Several of the original states ceded land , over a several year period, to the Federal government, which in turn became the Northwest Territory, Southwest Territory , and Mississippi Territory.

In , Texas ceded a large swath of land to the federal government. Additionally, Massachusetts and Virginia on two occasions , have lost land, in each instance to form a new state.

There have been numerous other minor adjustments to state boundaries over the years due to improved surveys, resolution of ambiguous or disputed boundary definitions, or minor mutually agreed boundary adjustments for administrative convenience or other purposes.

Supreme Court has had to settle state border disputes. One notable example is the case New Jersey v. States may be grouped in regions; there are many variations and possible groupings.

Many are defined in law or regulations by the federal government. For example, the United States Census Bureau defines four statistical regions, with nine divisions.

From Wikipedia, the free encyclopedia. Further information on each U. List of states and territories of the United States. State governments of the United States.

State constitution United States. State legislature United States. State court United States. Federalism in the United States. Admission to the Union.

Historic regions of the United States and List of U. District of Columbia statehood movement. Secession in the United States. List of state and territory name etymologies of the United States.

List of regions of the United States. April 1, to July 1, ". Census Bureau, Population Division. Archived from the original on April 9, Retrieved March 14, Archived from the original on March 16, Archived from the original on July 24, Retrieved January 12, Archived from the original on October 21, This can be done crudely by counting squares on graph paper or more precisely by integration.

The integration formula is written as:. Care must be taken to make sure that the integral converges. But the mean may be finite even if the function itself tends to infinity at some points.

Angles , times of day, and other cyclical quantities require modular arithmetic to add and otherwise combine numbers. In all these situations, there will not be a unique mean.

For example, the times an hour before and after midnight are equidistant to both midnight and noon. It is also possible that no mean exists.

Consider a color wheel -- there is no mean to the set of all colors. In these situations, you must decide which mean is most useful.

You can do this by adjusting the values before averaging, or by using a specialized approach for the mean of circular quantities.

It is sometimes also known as the Karcher mean named after Hermann Karcher. The sample mean is a random variable , not a constant, since its calculated value will randomly differ depending on which members of the population are sampled, and consequently it will have its own distribution.

For a random sample of n independent observations, the expected value of the sample mean is. If the population is normally distributed , then the sample mean is normally distributed:.

This follows from the central limit theorem. From Wikipedia, the free encyclopedia. This article is about the mathematical concept.

For other uses, see Mean disambiguation. For the state of being mean or cruel, see meanness. For a broader coverage of this topic, see average.

Inequality of arithmetic and geometric means. Mean of a function. Standard error of the mean. Johnson and Patricia J. Retrieved 16 March



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