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125-517: TIMSS is one of the studies established by IEA aimed at allowing educational systems worldwide to compare students' educational achievement and learn from the experiences of others in designing effective education policy. This assessment was first conducted in 1995, and has been administered every four years thereafter. Therefore, some of the participating educational systems have trend data across assessments from 1995 to 2019. TIMSS assesses 4th and 8th grade students, while TIMSS Advanced assesses students in

250-425: 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 . The Fréchet mean gives a manner for determining the "center" of a mass distribution on a surface or, more generally, Riemannian manifold . Unlike many other means,

375-421: A probability distribution is the long-run arithmetic average value of a random variable having that distribution. If the random variable is denoted by X {\displaystyle X} , then the mean is also known as the expected value of X {\displaystyle X} (denoted E ( X ) {\displaystyle E(X)} ). For a discrete probability distribution ,

500-400: A truncated mean . It involves discarding given parts of the data at the top or the bottom end, typically an equal amount at each end and then taking the arithmetic mean of the remaining data. The number of values removed is indicated as a percentage of the total number of values. The interquartile mean is a specific example of a truncated mean. It is simply the arithmetic mean after removing

625-562: A " Special Relationship " with the United Kingdom and strong ties with Canada , Australia , New Zealand , the Philippines , Japan , South Korea , Israel , and several European Union countries ( France , Italy , Germany , Spain , and Poland ). The U.S. works closely with its NATO allies on military and national security issues, and with countries in the Americas through

750-642: A comprehensive assessment of mathematics, science and reading for the countries participating in both studies. The sixth cycle was conducted in 2015, and the results were released in 2016; the data set was published in February 2017. TIMSS 2015 included data collected from parents for the first time. TIMSS Advanced, previously conducted in 1995 and 2008, was also conducted in 2015, and assessed final-year secondary students' achievement in advanced mathematics and physics. Policy-relevant data about curriculum emphasis, technology use, and teacher preparation and training accompanies

875-572: A decentralized government that operated until 1789. After the British surrender at the siege of Yorktown in 1781 American sovereignty was internationally recognized by the Treaty of Paris (1783), through which the U.S. gained territory stretching west to the Mississippi River, north to present-day Canada, and south to Spanish Florida . The Northwest Ordinance (1787) established the precedent by which

1000-407: A few prominent industrialists , largely by their formation of trusts and monopolies to prevent competition. Tycoons led the nation's expansion in the railroad , petroleum , and steel industries. The United States emerged as a pioneer of the automotive industry . These changes were accompanied by significant increases in economic inequality , slum conditions , and social unrest , creating

1125-417: A function f ( x ) {\displaystyle f(x)} . Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section. This can be done crudely by counting squares on graph paper, or more precisely by integration . The integration formula is written as: In this case, care must be taken to make sure that

1250-518: A given group of data , illustrating the magnitude and sign of the data set . Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The arithmetic mean , also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x 1 , x 2 , ..., x n is typically denoted using an overhead bar , x ¯ {\displaystyle {\bar {x}}} . If

1375-644: A global reach. The U.S. is a founding member of the World Bank , Organization of American States , NATO , and the United Nations , as well as a permanent member of the UN Security Council . The first documented use of the phrase "United States of America" is a letter from January 2, 1776. Stephen Moylan , a Continental Army aide to General George Washington , wrote to Joseph Reed , Washington's aide-de-camp , seeking to go "with full and ample powers from

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1500-399: A list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} , usually denoted by x ¯ {\displaystyle {\bar {x}}} , is the sum of the sampled values divided by

1625-421: A measure of central tendency ). The mean of a set of observations is the arithmetic average of the values; however, for skewed distributions , the mean is not necessarily the same as the middle value (median), or the most likely value (mode). For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast,

1750-513: A methodology to rescale 14 different international comparisons of math and/or science achievement to make them comparable. This includes the FIMS, FISS, and PISA, mentioned above, with TIMSS. This methodology is disputed amongst experts. Quantitative methods used in educational and psychological measurement disagree with the approach as it is basically only a linear scale transformation that cannot ensure or examine whether PISA and TIMSS scores are based on

1875-583: A period of heightened, overt racism following Reconstruction, a time often called the nadir of American race relations . A series of Supreme Court decisions, including Plessy v. Ferguson , emptied the Fourteenth and Fifteenth Amendments of their force, allowing Jim Crow laws in the South to remain unchecked, sundown towns in the Midwest, and segregation in communities across the country , which would be reinforced by

2000-488: A prominent leader in the early 1960s. The Great Society plan of President Lyndon Johnson 's administration resulted in groundbreaking and broad-reaching laws, policies and a constitutional amendment to counteract some of the worst effects of lingering institutional racism . The counterculture movement in the U.S. brought significant social changes, including the liberalization of attitudes toward recreational drug use and sexuality . It also encouraged open defiance of

2125-518: A sense of manifest destiny . The Missouri Compromise attempted to balance the desire of northern states to prevent the expansion of slavery into new territories with that of southern states to extend it, admitting Missouri as a slave state and Maine as a free state. It further prohibited slavery in all other lands of the Louisiana Purchase north of the 36°30′ parallel . As Americans expanded further into land inhabited by Native Americans,

2250-485: A wide range of other notions of mean are often used in geometry and mathematical analysis ; examples are given below. In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians because of their importance in geometry and music. The arithmetic mean (or simply mean or average ) of

2375-457: A year). Juvenile correctional facilities are operated by local or state governments and serve as longer-term placements for any minor adjudicated as delinquent and ordered by a judge to be confined. As of January 2023, the United States has the sixth-highest per capita incarceration rate in the world—531 people per 100,000 inhabitants—and the largest prison and jail population in

2500-486: Is an average which is useful for sets of numbers which are defined in relation to some unit , as in the case of speed (i.e., distance per unit of time): For example, the harmonic mean of the five values: 4, 36, 45, 50, 75 is If we have five pumps that can empty a tank of a certain size in respectively 4, 36, 45, 50, and 75 minutes, then the harmonic mean of 15 {\displaystyle 15} tells us that these five different pumps working together will pump at

2625-571: Is believed to be the first widespread culture in the Americas. Over time, indigenous North American cultures grew increasingly sophisticated, and some, such as the Mississippian culture , developed agriculture , architecture , and complex societies . In the post-archaic period , the Mississippian cultures were located in the midwestern , eastern , and southern regions, and the Algonquian in

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2750-492: Is known as the presidential system , in contrast to the parliamentary system , where the executive is part of the legislative body. Many countries around the world imitated this aspect of the 1789 Constitution of the United States , especially in the Americas. The Constitution is silent on political parties. However, they developed independently in the 18th century with the Federalist and Anti-Federalist parties. Since then,

2875-438: Is now the United States experienced conflicts with Native Americans, they also engaged in trade, exchanging European tools for food and animal pelts. Relations ranged from close cooperation to warfare and massacres. The colonial authorities often pursued policies that forced Native Americans to adopt European lifestyles, including conversion to Christianity. Along the eastern seaboard, settlers trafficked African slaves through

3000-487: Is the probability density function . In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the Lebesgue integral of the random variable with respect to its probability measure . The mean need not exist or be finite; for some probability distributions the mean is infinite ( +∞ or −∞ ), while for others the mean is undefined . The generalized mean , also known as

3125-542: Is the federal agency charged with addressing most environmental-related issues . The idea of wilderness has shaped the management of public lands since 1964, with the Wilderness Act . The Endangered Species Act of 1973 provides a way to protect threatened and endangered species and their habitats. The United States Fish and Wildlife Service implements and enforces the Act. In 2024, the U.S. ranked 34th among 180 countries in

3250-569: The Allies , helping to turn the tide against the Central Powers . In 1920, a constitutional amendment granted nationwide women's suffrage . During the 1920s and '30s, radio for mass communication and the invention of early television transformed communications nationwide. The Wall Street Crash of 1929 triggered the Great Depression , which President Franklin D. Roosevelt responded to with

3375-548: The Atlantic slave trade . The original Thirteen Colonies that would later found the United States were administered as possessions of Great Britain , and had local governments with elections open to most white male property owners . The colonial population grew rapidly, eclipsing Native American populations; by the 1770s, the natural increase of the population was such that only a small minority of Americans had been born overseas. The colonies' distance from Britain allowed for

3500-773: The Bering land bridge more than 12,000 years ago, and formed various civilizations and societies . British colonization led to the first settlement of the Thirteen Colonies in Virginia in 1607. Clashes with the British Crown over taxation and political representation sparked the American Revolution , with the Second Continental Congress formally declaring independence on July 4, 1776. Following its victory in

3625-529: The Environmental Performance Index . The country joined the Paris Agreement on climate change in 2016 and has many other environmental commitments. The United States is a federal republic of 50 states and a separate federal capital district, Washington, D.C. It also asserts sovereignty over five unincorporated territories and several uninhabited island possessions . The U.S. is

3750-493: The Federal Bureau of Investigation (FBI) and the U.S. Marshals Service have national jurisdiction and specialized duties, such as protecting civil rights , national security and enforcing U.S. federal courts ' rulings and federal laws. State courts conduct most civil and criminal trials, and federal courts handle designated crimes and appeals of state court decisions . There is no unified "criminal justice system" in

3875-688: The Great Lakes , Mississippi River and Gulf of Mexico . British colonization of the East Coast began with the Virginia Colony (1607) and Plymouth Colony (1620). The Mayflower Compact and the Fundamental Orders of Connecticut established precedents for representative self-governance and constitutionalism that would develop throughout the American colonies. While European settlers in what

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4000-701: The Great Lakes region and along the Eastern Seaboard , while the Hohokam culture and Ancestral Puebloans inhabited the southwest . Native population estimates of what is now the United States before the arrival of European immigrants range from around 500,000 to nearly 10 million. Christopher Columbus began exploring the Caribbean for Spain in 1492, leading to Spanish-speaking settlements and missions from Puerto Rico and Florida to New Mexico and California . France established its own settlements along

4125-583: The House of Representatives , a lower house based on population; and the Senate , an upper house based on equal representation for each state. Federalism provides substantial autonomy to the 50 states, while American values are based on a democratic political tradition that draws its inspiration from the European Enlightenment movement . One of the world's most developed countries , the United States has had

4250-580: The Midwest . At the same time, about one million French Canadians migrated from Quebec to New England . During the Great Migration , millions of African Americans left the rural South for urban areas in the North. Alaska was purchased from Russia in 1867. The Compromise of 1877 effectively ended Reconstruction and white supremacists took local control of Southern politics . African Americans endured

4375-672: The National Park Service and other agencies. About 28% of the country's land is publicly owned and federally managed, primarily in the Western States . Most of this land is protected , though some is leased for commercial use, and less than one percent is used for military purposes. Environmental issues in the United States include debates on non-renewable resources and nuclear energy , air and water pollution , biodiversity , logging and deforestation , and climate change . The U.S. Environmental Protection Agency (EPA)

4500-634: The New Deal , a series of sweeping programs and public works projects combined with financial reforms and regulations . All were intended to protect against future economic depressions. Initially neutral during World War II , the U.S. began supplying war materiel to the Allies of World War II in March 1941 and entered the war in December after the Empire of Japan 's attack on Pearl Harbor . The U.S. developed

4625-759: The Organization of American States and the United States–Mexico–Canada Free Trade Agreement . In South America, Colombia is traditionally considered to be the closest ally of the United States. The U.S. exercises full international defense authority and responsibility for Micronesia , the Marshall Islands , and Palau through the Compact of Free Association . It has increasingly conducted strategic cooperation with India , but its ties with China have steadily deteriorated. Since 2014,

4750-638: The Pentium microprocessor in accordance with Moore's law , rechargeable lithium-ion batteries , the first gene therapy trial, and cloning either emerged in the U.S. or were improved upon there. The Human Genome Project was formally launched in 1990, while Nasdaq became the first stock market in the United States to trade online in 1998. In the Gulf War of 1991, an American-led international coalition of states expelled an Iraqi invasion force that had occupied neighboring Kuwait . The September 11 attacks on

4875-523: The Soviet Union's collapse and the end of the Cold War in 1991, the U.S. emerged as the world's sole superpower , wielding significant geopolitical influence globally . The U.S. national government is a presidential constitutional federal republic and liberal democracy with three separate branches : legislative , executive , and judicial . It has a bicameral national legislature composed of

5000-576: The Spanish–American War . (The Philippines was granted full independence from the U.S. on July 4, 1946, following World War II. Puerto Rico and Guam have remained U.S. territories.) American Samoa was acquired by the United States in 1900 after the Second Samoan Civil War . The U.S. Virgin Islands were purchased from Denmark in 1917. The United States entered World War I alongside

5125-670: The cotton gin made the institution increasingly profitable for Southern elites . This sectional conflict regarding slavery culminated in the American Civil War (1861–1865). Eleven slave states seceded and formed the Confederate States of America , while the other states remained in the Union . War broke out in April 1861 after the Confederates bombarded Fort Sumter . After

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5250-524: The fall of communism and the collapse of the Soviet Union , which marked the end of the Cold War and left the United States as the world's sole superpower . The 1990s saw the longest recorded economic expansion in American history , a dramatic decline in U.S. crime rates , and advances in technology . Throughout this decade, technological innovations such as the World Wide Web , the evolution of

5375-469: The highest disposable household income per capita among OECD countries. As of February 2024, the total federal government debt was $ 34.4 trillion. Mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency ") in mathematics , especially in statistics . Each attempts to summarize or typify

5500-445: The largest nominal GDP since about 1890 and accounted for over 15% of the global economy in 2023. It possesses by far the largest amount of wealth of any country and has the highest disposable household income per capita among OECD countries. The U.S. ranks among the world's highest in economic competitiveness , productivity , innovation , human rights , and higher education . Its hard power and cultural influence have

5625-695: The 1775 Battles of Lexington and Concord , igniting the American Revolutionary War . At the Second Continental Congress , the colonies appointed George Washington commander-in-chief of the Continental Army , and created a committee that named Thomas Jefferson to draft the Declaration of Independence . Two days after passing the Lee Resolution to create an independent nation the Declaration

5750-408: The 1775–1783 Revolutionary War , the country continued to expand westward across North America , resulting in the dispossession of native inhabitants . As more states were admitted , a North–South division over slavery led to the secession of the Confederate States of America , which fought states remaining in the Union in the 1861–1865 American Civil War . With the victory and preservation of

5875-515: The 2010s, political polarization in the country increased between liberal and conservative factions. This polarization was capitalized upon in the January 2021 Capitol attack , when a mob of insurrectionists entered the U.S. Capitol and sought to prevent the peaceful transfer of power in an attempted self-coup d'état . The United States is the world's third-largest country by total area behind Russia and Canada. The 48 contiguous states and

6000-580: The American West have an alpine climate . The climate is arid in the Southwest, Mediterranean in coastal California , and oceanic in coastal Oregon , Washington , and southern Alaska . Most of Alaska is subarctic or polar . Hawaii , the southern tip of Florida and U.S. territories in the Caribbean and Pacific are tropical . States bordering the Gulf of Mexico are prone to hurricanes, and most of

6125-470: The Declaration of Independence on July 4, 1776. The term "United States" and the initialism "U.S.", used as nouns or as adjectives in English, are common short names for the country. The initialism "USA", a noun, is also common. "United States" and "U.S." are the established terms throughout the U.S. federal government , with prescribed rules. In English, the term "America" rarely refers to topics unrelated to

6250-557: The District of Columbia occupy a combined area of 3,119,885 square miles (8,080,470 km ). The coastal plain of the Atlantic seaboard gives way to inland forests and rolling hills in the Piedmont plateau region. The Appalachian Mountains and the Adirondack massif separate the East Coast from the Great Lakes and the grasslands of the Midwest . The Mississippi River System ,

6375-663: The Elder concluded that major military resources needed to be devoted to North America to win the war against France. The British colonies' position as an integral part of the British Empire became more apparent during the war, with British military and civilian officials becoming a more significant presence in American life. Following their victory in the French and Indian War, Britain began to assert greater control over local colonial affairs, resulting in colonial political resistance ; one of

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6500-501: The Fréchet mean is defined on a space whose elements cannot necessarily be added together or multiplied by scalars. It is sometimes also known as the Karcher mean (named after Hermann Karcher). In geometry, there are thousands of different definitions for the center of a triangle that can all be interpreted as the mean of a triangular set of points in the plane. This is an approximation to

6625-586: The IEA to create TIMSS, which was first administered in 1995. It was the largest international student assessment study of its time and evaluated students in five grades. In the second cycle (1999) only eighth-grade students were tested. In the next cycles (2003, 2007, 2011, and 2015) both 4th and 8th grade students were assessed. The 2011 cycle was performed in the same year as the IEA's Progress in International Reading Literacy Study (PIRLS), offering

6750-693: The IEA, the study was conducted by the US National Center for Education Statistics, and the US Department of Education under a contract with LessonLab, Inc. of Los Angeles, California. TIMSS depends on the collaboration of a large number of individuals and organizations around the world including the TIMSS & PIRLS International Study Center at Boston College , IEA's offices in Amsterdam and Hamburg , Statistics Canada , and Educational Testing Service (ETS). In

6875-664: The January 1863 Emancipation Proclamation , many freed slaves joined the Union army . The war began to turn in the Union's favor following the 1863 Siege of Vicksburg and Battle of Gettysburg , and the Confederacy surrendered in 1865 after the Union's victory in the Battle of Appomattox Court House . The Reconstruction era followed the war. After the assassination of President Abraham Lincoln , Reconstruction Amendments were passed to protect

7000-476: The Rocky Mountains, the Yellowstone Caldera , is the continent's largest volcanic feature. In 2021, the United States had 8% of global permanent meadows and pastures and 10% of cropland. With its large size and geographic variety, the United States includes most climate types. East of the 100th meridian , the climate ranges from humid continental in the north to humid subtropical in the south. The western Great Plains are semi-arid . Many mountainous areas of

7125-594: The TIMSS 2019 Encyclopedia: Education Policy and Curriculum in Mathematics and Science. TIMSS 2019 marked the transition to a digital assessment format, allowing for new and innovative item types. In the digital assessment, students solved problems by interacting with shapes and patterns, arranging items on the screen, dragging and dropping items, and drawing. The digital version of TIMSS 2019 also introduced Problem Solving and Inquiry tasks that simulated real-world and laboratory situations and called for students to integrate and apply process skills and content knowledge. Half of

7250-457: The TIMSS Advanced results. The seventh cycle of TIMSS was conducted in 2019 and marked the beginning of the transition to a digital assessment format, with the digital assessment administered to half of participating countries, and the paper assessment administered to the remaining half. 64 countries and 8 benchmarking systems participating in TIMSS 2019. Results were released in December 2020. Preparations are underway for TIMSS 2023. Along with

7375-410: The TIMSS NAEP link, or IEA's Rosetta Stone. Wu (2003, 2010) has shown that TIMSS and PISA do not produce exchangeable scores. One reason may be reading load even for mathematics and science items. TIMSS questions focus on the mathematics curricula taught around the world as seen in TIMSS example items, while PISA attempts to assess mathematics embedded in descriptions of situations encountered outside of

7500-451: The U.S. has become a key ally of Ukraine ; it has also provided the country with significant military equipment and other support in response to Russia's 2022 invasion . The president is the commander-in-chief of the United States Armed Forces and appoints its leaders, the secretary of defense and the Joint Chiefs of Staff . The Department of Defense , which is headquartered at the Pentagon near Washington, D.C., administers five of

7625-661: The U.S. territories." Despite disparate systems of confinement, four main institutions dominate: federal prisons , state prisons , local jails, and juvenile correctional facilities . Federal prisons are run by the Federal Bureau of Prisons and hold people who have been convicted of federal crimes, including pretrial detainees. State prisons, run by the official department of correction of each state, hold sentenced people serving prison time (usually longer than one year) for felony offenses. Local jails are county or municipal facilities that incarcerate defendants prior to trial; they also hold those serving short sentences (typically under

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7750-402: The United States and the peaceful transfer of power . The Louisiana Purchase of 1803 from France nearly doubled the territory of the United States. Lingering issues with Britain remained , leading to the War of 1812 , which was fought to a draw. Spain ceded Florida and its Gulf Coast territory in 1819. In the late 18th century, American settlers began to expand westward , many with

7875-541: The United States entered the Cold War, where geopolitical tensions between the U.S. and the Soviet Union led the two countries to dominate world affairs . The U.S. utilized the policy of containment to limit the USSR's sphere of influence, and prevailed in the Space Race , which culminated with the first crewed Moon landing in 1969. Domestically, the U.S. experienced economic growth , urbanization , and population growth following World War II . The civil rights movement emerged, with Martin Luther King Jr. becoming

8000-495: The United States has operated as a de facto two-party system , though the parties in that system have been different at different times. The two main national parties are presently the Democratic and the Republican . The former is perceived as relatively liberal in its political platform while the latter is perceived as relatively conservative . In the American federal system , sovereign powers are shared between two levels of elected government: national and state. People in

8125-402: The United States in 2001 by the pan-Islamist militant organization al-Qaeda led to the war on terror , and subsequent military interventions in Afghanistan and Iraq . The cultural impact of the attacks was profound and long-lasting. The U.S. housing bubble culminated in 2007 with the Great Recession , the largest economic contraction since the Great Depression. Coming to a head in

8250-415: The United States of America to Spain" to seek assistance in the Revolutionary War effort. The first known public usage is an anonymous essay published in the Williamsburg newspaper, The Virginia Gazette , on April 6, 1776. By June 1776, the "United States of America" appeared in the Articles of Confederation and the Declaration of Independence . The Second Continental Congress adopted

8375-490: The United States, slavery was abolished nationally . By 1900, the country had established itself as a great power , a status solidified after its involvement in World War I . After Japan 's attack on Pearl Harbor in December 1941, the U.S. entered World War II . Its aftermath left the U.S. and the Soviet Union as the world's two superpowers and led to the Cold War , during which both countries struggled for ideological dominance and international influence . Following

8500-442: The United States, TIMSS is conducted by the National Center for Education Statistics of the US Department of Education. Data for US students is further tracked for ethnic and racial groups. TIMSS is mainly funded by the participating countries. Also, the US National Center for Education Statistics of the US Department of Education and the World Bank provide major support funding for the assessments. Hanushek and Woessmann developed

8625-434: The United States, despite the usage of "the Americas " as the totality of North and South America. "The States" is an established colloquial shortening of the name, used particularly from abroad; "stateside" is the corresponding adjective or adverb. The first inhabitants of North America migrated from Siberia across the Bering land bridge about 12,000 years ago; the Clovis culture , which appeared around 11,000 BC,

8750-478: The United States, except Iran , North Korea , and Bhutan . Though Taiwan does not have formal diplomatic relations with the U.S., it maintains close unofficial relations. The United States regularly supplies Taiwan with military equipment to deter potential Chinese aggression. Its geopolitical attention also turned to the Indo-Pacific when the United States joined the Quadrilateral Security Dialogue with Australia, India, and Japan. The United States has

8875-509: The United States. The American prison system is largely heterogenous, with thousands of relatively independent systems operating across federal, state, local, and tribal levels. In 2023, "these systems [held] almost 2 million people in 1,566 state prisons, 98 federal prisons, 3,116 local jails, 1,323 juvenile correctional facilities, 181 immigration detention facilities, and 80 Indian country jails, as well as in military prisons , civil commitment centers, state psychiatric hospitals, and prisons in

9000-528: The classroom, see PISA examples. United States The United States of America ( USA ), commonly known as the United States ( U.S. ) or America , is a country primarily located in North America . It is a federal union of 50 states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the states of Alaska to

9125-759: The complex sample structure of the databases when calculating the statistics and their standard errors. It also allows researchers to estimate achievement scores and their standard errors. For an overview of the IEA study results and interpretation of information, see IEA's Data Visualizer. TIMSS 2019 was the seventh cycle of TIMSS and reported overall achievement as well as results according to international benchmarks, by major content domains (number, algebra, and geometry in mathematics, and earth science, biology, and chemistry in science) and by cognitive domains (knowing, applying, reasoning). TIMSS 2019 collected detailed information about curriculum and curriculum implementation of participating countries and published this information

9250-453: The contiguous United States are in the State of California, about 84 miles (135 km) apart. At an elevation of 20,310 feet (6,190.5 m), Alaska's Denali is the highest peak in the country and continent. Active volcanoes are common throughout Alaska's Alexander and Aleutian Islands , and Hawaii consists of volcanic islands. The supervolcano underlying Yellowstone National Park in

9375-549: The country's GDP. The U.S. has 42% of the world's nuclear weapons —the second-largest share after Russia. The United States has the third-largest combined armed forces in the world, behind the Chinese People's Liberation Army and Indian Armed Forces . The military operates about 800 bases and facilities abroad, and maintains deployments greater than 100 active duty personnel in 25 foreign countries. State defense forces (SDFs) are military units that operate under

9500-464: The country's territory would expand with the admission of new states , rather than the expansion of existing states. The U.S. Constitution was drafted at the 1787 Constitutional Convention to overcome the limitations of the Articles. It went into effect in 1789, creating a federal republic governed by three separate branches that together ensured a system of checks and balances . George Washington

9625-699: The development of self-governance, and the First Great Awakening , a series of Christian revivals , fueled colonial interest in religious liberty . For a century, the American colonists had been providing their own troops and materiel in conflicts with indigenous peoples allied with Britain's colonial rivals , especially France, and the Americans had begun to develop a sense of self-defense and self-reliance separate from Britain. The French and Indian War (1754–1763) took on new significance for all North American colonists after Parliament under William Pitt

9750-858: The development of the TIMSS assessments and questionnaires, and describes the methods used. The TIMSS 2019 User Guide for the International Database describes the content and format of the data in the TIMSS 2019 International Database The IEA has developed an application for working with data from TIMSS and other IEA large-scale assessments called the IEA International Database (IDB) Analyzer. This application allows researchers to combine data files and facilitates some types of statistical analysis (such as computing means , percentages , percentiles , correlations , and estimating single level multiple linear regression ). The application takes into account

9875-446: The education systems in each participating country, including the mathematics and science curriculum, professional development requirements for teachers, and methods of monitoring student progress in mathematics and science. Each country's "chapter" in the encyclopedia was authored by that country's TIMSS representative. In TIMSS 2015, nationally representative samples of students in 57 countries and 7 benchmarking entities participated in

10000-474: The eighth grade in 38 educational systems; there was no study done for the fourth grade in that year. In TIMSS 1995, there were 41 educational systems in five grades (third, fourth, seventh, eighth, and the final year of secondary school). The TIMSS 1999 Video Study was a study of eighth-grade mathematics and science teaching in seven countries. The study involved videotaping and analyzing teaching practices in more than one thousand classrooms. In conjunction with

10125-564: The environment for labor unions to begin to flourish . This period eventually ended with the advent of the Progressive Era , which was characterized by significant reforms. Pro-American elements in Hawaii overthrew the Hawaiian monarchy ; the islands were annexed in 1898. That same year, Puerto Rico , the Philippines , and Guam were ceded to the U.S. by Spain after the latter's defeat in

10250-527: The federal government often applied policies of Indian removal or assimilation . The Trail of Tears (1830–1850) was a U.S. government policy that forcibly removed and displaced most Native Americans living east of the Mississippi River to lands far to the west. These and earlier organized displacements prompted a long series of American Indian Wars west of the Mississippi. The Republic of Texas

10375-636: The final year of secondary education (FS) under the auspices of the International Association for the Evaluation of Educational Achievement (IEA). This was followed in 1970–1971 by the First International Science Study (FISS) for students aged 10, 14, and FS. Fourteen countries tested 10-year-olds; 16 countries tested the older two groups. These were replicated between 1980 and 1984. These early studies were revised and combined by

10500-492: The final year of secondary school in advanced mathematics and physics. "Eighth grade" in the United States is approximately 13–14 years of age and equivalent to: "Fourth grade" in the United States is approximately equivalent to 9–10 years of age and equivalent to: A precursor to TIMSS was the First International Mathematics Study (FIMS) performed in 1964 in 11 countries for students aged 13 and in

10625-590: The first nuclear weapons and used them against the Japanese cities of Hiroshima and Nagasaki in August 1945, ending the war. The United States was one of the " Four Policemen " who met to plan the post-war world , alongside the United Kingdom , Soviet Union , and China . The U.S. emerged relatively unscathed from the war, with even greater economic power and international political influence . After World War II,

10750-425: The fourth grade assessment, the eighth grade assessment, or both. TIMSS 2011 had 52 participating educational systems for the fourth grade and 45 for the eighth grade. In TIMSS 2007, 43 educational systems participated in the fourth grade and 56 educational systems in the eighth grade. In TIMSS 2003, there were 26 educational systems for the fourth grade and 48 for the eighth grade. In 1999, TIMSS only focused on

10875-649: The fourth grade in TIMSS 1995 can be compared with the results of the eighth grade in TIMSS 1999, as fourth graders had become eighth graders in the next cycle of study. The collected information is presented in different formats. For example, for TIMSS 2019 the results are presented as TIMSS 2019 International Results in Mathematics and Science TIMSS 2019 International Results in Mathematics and Science. The TIMSS 2019 Encyclopedia provides an overview of how mathematics and science are taught in each participating country. Methods and Procedures: TIMSS 2019 Technical Report documents

11000-443: 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

11125-463: The integration of Army National Guard units and personnel into the U.S. Army and (since 1947) the U.S. Air Force. There are about 18,000 U.S. police agencies from local to national level in the United States. Law in the United States is mainly enforced by local police departments and sheriff departments in their municipal or county jurisdictions. The state police departments have authority in their respective state , and federal agencies such as

11250-411: The lowest and the highest quarter of values. assuming the values have been ordered, so is simply a specific example of a weighted mean for a specific set of weights. In some circumstances, mathematicians may calculate a mean of an infinite (or even an uncountable ) set of values. This can happen when calculating the mean value y avg {\displaystyle y_{\text{avg}}} of

11375-422: The mean and size of sample i {\displaystyle i} respectively. In other applications, they represent a measure for the reliability of the influence upon the mean by the respective values. Sometimes, a set of numbers might contain outliers (i.e., data values which are much lower or much higher than the others). Often, outliers are erroneous data caused by artifacts . In this case, one can use

11500-598: The mean is given by ∑ x P ( x ) {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and P ( x ) {\displaystyle P(x)} is the probability mass function . For a continuous distribution , the mean is ∫ − ∞ ∞ x f ( x ) d x {\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx} , where f ( x ) {\displaystyle f(x)}

11625-409: The median income is the level at which half the population is below and half is above. The mode income is the most likely income and favors the larger number of people with lower incomes. While the median and mode are often more intuitive measures for such skewed data, many skewed distributions are in fact best described by their mean, including the exponential and Poisson distributions. The mean of

11750-477: The military draft (leading to the end of conscription in 1973) and wide opposition to U.S. intervention in Vietnam (with the U.S. totally withdrawing in 1975). A societal shift in the roles of women was significantly responsible for the large increase in female paid labor participation during the 1970s, and by 1985 the majority of American women aged 16 and older were employed. The late 1980s and early 1990s saw

11875-612: The most attractive to the population are the most vulnerable. The U.S. is one of 17 megadiverse countries containing large numbers of endemic species : about 17,000 species of vascular plants occur in the contiguous United States and Alaska, and over 1,800 species of flowering plants are found in Hawaii, few of which occur on the mainland. The United States is home to 428 mammal species, 784 birds, 311 reptiles, 295 amphibians , and around 91,000 insect species. There are 63 national parks , and hundreds of other federally managed parks, forests, and wilderness areas , managed by

12000-642: The most violent, the California genocide of thousands of Native inhabitants, lasted into the early 1870s, just as additional western territories and states were created. During the colonial period, slavery had been legal in the American colonies , though the practice began to be significantly questioned during the American Revolution. States in the North enacted abolition laws , though support for slavery strengthened in Southern states , as inventions such as

12125-585: The northwest and the archipelagic Hawaii in the Pacific Ocean . The United States also asserts sovereignty over five major island territories and various uninhabited islands . The country has the world's third-largest land area , largest exclusive economic zone , and third-largest population , exceeding 334 million. Its three largest metropolitan areas are New York , Los Angeles , and Chicago , and its three most populous states are California , Texas , and Florida . Paleo-Indians migrated across

12250-429: The number of items in the sample. For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is: The geometric mean is an average that is useful for sets of positive numbers, that are interpreted according to their product (as is the case with rates of growth) and not their sum (as is the case with the arithmetic mean): For example, the geometric mean of five values: 4, 36, 45, 50, 75 is: The harmonic mean

12375-475: The numbers are from observing a sample of a larger group , the arithmetic mean is termed the sample mean ( x ¯ {\displaystyle {\bar {x}}} ) to distinguish it from the group mean (or expected value ) of the underlying distribution, denoted μ {\displaystyle \mu } or μ x {\displaystyle \mu _{x}} . Outside probability and statistics,

12500-403: The overall students' achievement data, TIMSS comprehensive assessments include data on student performance in various mathematics and science domains (algebra, geometry, biology, chemistry, etc.) and on performance in the problem solving challenges in each of these contexts. In addition, TIMSS provides contextual data on crucial curricular, instructional, and resource-related factors that can impact

12625-517: The parameter m , the following types of means are obtained: This can be generalized further as the generalized f -mean and again a suitable choice of an invertible f will give The weighted arithmetic mean (or weighted average) is used if one wants to combine average values from different sized samples of the same population: Where x i ¯ {\displaystyle {\bar {x_{i}}}} and w i {\displaystyle w_{i}} are

12750-470: The participating countries took the paper version of TIMSS and half of the participating countries took the digital version of TIMSS. TIMSS 2019 results are summarized in TIMSS 2019 International Results in Mathematics and Science. This detailed report presents achievement and contextual data from participating countries and benchmarking entities. The TIMSS 2019 Encyclopedia: Education Policy and Curriculum in Mathematics and Science describes various features of

12875-408: The policy of redlining later adopted by the federal Home Owners' Loan Corporation . An explosion of technological advancement accompanied by the exploitation of cheap immigrant labor led to rapid economic expansion during the late 19th and early 20th centuries , allowing the United States to outpace the economies of England, France, and Germany combined. This fostered the amassing of power by

13000-511: The power mean or Hölder mean, is an abstraction of the quadratic , arithmetic, geometric, and harmonic means. It is defined for a set of n positive numbers x i by x ¯ ( m ) = ( 1 n ∑ i = 1 n x i m ) 1 m {\displaystyle {\bar {x}}(m)=\left({\frac {1}{n}}\sum _{i=1}^{n}x_{i}^{m}\right)^{\frac {1}{m}}} By choosing different values for

13125-553: The primary colonial grievances was a denial of their rights as Englishmen , particularly the right to representation in the British government that taxed them . To demonstrate their dissatisfaction and resolve, the First Continental Congress met in 1774 and passed the Continental Association , a colonial boycott of British goods that proved effective. The British attempt to then disarm the colonists resulted in

13250-565: The rights of African Americans . National infrastructure, including transcontinental telegraph and railroads , spurred growth in the American frontier . From 1865 through 1917 an unprecedented stream of immigrants arrived in the United States, including 24.4 million from Europe. Most came through the port of New York City , and New York City and other large cities on the East Coast became home to large Jewish , Irish , and Italian populations, while many Germans and Central Europeans moved to

13375-596: The rocky Great Basin and Chihuahua , Sonoran , and Mojave deserts. In the northwest corner of Arizona , carved by the Colorado River over millions of years, is the Grand Canyon , a steep-sided canyon and popular tourist destination known for its overwhelming visual size and intricate, colorful landscape. The Sierra Nevada and Cascade mountain ranges run close to the Pacific coast . The lowest and highest points in

13500-409: The same or at least comparable measurement constructs: The numerical values used to measure shoe size and intelligence can be transformed so that both have the same arithmetic mean and standard deviation, but they still represent two very different characteristics. The equivalency of what is being measured needs to be established in linking studies that utilize well-designed joint data collections such as

13625-407: The same rate as much as five pumps that can each empty the tank in 15 {\displaystyle 15} minutes. AM, GM, and HM satisfy these inequalities: Equality holds if all the elements of the given sample are equal. In descriptive statistics , the mean may be confused with the median , mode or mid-range , as any of these may incorrectly be called an "average" (more formally,

13750-400: The same scale metrics, making it possible to measure growth or decline in countries' achievement distributions from assessment to assessment." Because TIMSS is administered in four-year cycles, it enables participating counties to use the results between the fourth and eighth grades to track the changes in achievement and certain background factors from an earlier study. For example, results of

13875-410: The scale was equivalent to one standard deviation of the distribution of achievement across all of the countries that participated in TIMSS 1995, and the scale midpoint of 500 was located at the mean of this international achievement distribution. The TIMSS achievement scales were first used for reporting TIMSS results with TIMSS 1995, and all results from subsequent TIMSS assessments have been reported on

14000-563: The six service branches, which are made up of the U.S. Army , Marine Corps , Navy , Air Force , and Space Force . The Coast Guard is administered by the Department of Homeland Security in peacetime and can be transferred to the Department of the Navy in wartime. The United States spent $ 916 billion on its military in 2023, which is by far the largest amount of any country , making up 37% of global military spending and accounting for 3.4% of

14125-528: The sole authority of a state government. SDFs are authorized by state and federal law but are under the command of the state's governor . They are distinct from the state's National Guard units in that they cannot become federalized entities. A state's National Guard personnel, however, may be federalized under the National Defense Act Amendments of 1933 , which created the Guard and provides for

14250-543: The states are also represented by local elected governments , which are administrative divisions of the states. States are subdivided into counties or county equivalents , and further divided into municipalities . The District of Columbia is a federal district containing the U.S. capital, Washington, D.C. . The federal district is an administrative division of the federal government. Federally recognized tribes govern 326 Indian reservations . The United States has an established structure of foreign relations, and it has

14375-504: The structure and responsibilities of the national federal government and its relationship with the individual states. The U.S. Constitution is the world's oldest national constitution still in effect (from March 4, 1789). Composed of three branches, all headquartered in Washington, D.C., the federal government is the national government of the United States. It is regulated by a strong system of checks and balances . The three-branch system

14500-493: The teaching and learning process. These data are gathered using student, teacher, school, and curriculum (national) questionnaires filled out by students, teachers, school principals and National Research Coordinators, respectively. According to the TIMSS 2019 Assessment Frameworks, "The TIMSS mathematics and science achievement scales were created with the first TIMSS assessment in 1995, separately for each subject and each grade. The scale units were established so that 100 points on

14625-565: The world's fourth-longest river system , runs predominantly north–south through the heart of the country. The flat and fertile prairie of the Great Plains stretches to the west, interrupted by a highland region in the southeast. The Rocky Mountains , west of the Great Plains, extend north to south across the country, peaking at over 14,000 feet (4,300 m) in Colorado . Farther west are

14750-567: The world's second-largest diplomatic corps as of 2024 . It is a permanent member of the United Nations Security Council , and home to the United Nations headquarters . The United States is a member of the G7 , G20 , and OECD intergovernmental organizations. Almost all countries have embassies and many have consulates (official representatives) in the country. Likewise, nearly all countries host formal diplomatic missions with

14875-444: The world's oldest surviving federation, and its presidential system of national government has been adopted, in whole or in part, by many newly independent states worldwide following their decolonization . It is a liberal representative democracy "in which majority rule is tempered by minority rights protected by law ". The Constitution of the United States serves as the country's supreme legal document , also establishing

15000-538: The world's tornadoes occur in the country , mainly in Tornado Alley . Overall, the United States receives more high-impact extreme weather incidents than any other country. Extreme weather became more frequent in the U.S. in the 21st century, with three times the number of reported heat waves as in the 1960s. In the American Southwest , droughts became more persistent and more severe. The regions considered as

15125-528: The world, with almost 2 million people incarcerated . An analysis of the World Health Organization Mortality Database from 2010 showed U.S. homicide rates "were 7 times higher than in other high-income countries, driven by a gun homicide rate that was 25 times higher". The U.S. has been the world's largest economy nominally since about 1890 . The 2023 nominal U.S. gross domestic product (GDP) of more than $ 27 trillion

15250-570: Was annexed in 1845, and the 1846 Oregon Treaty led to U.S. control of the present-day American Northwest . Victory in the Mexican–American War resulted in the 1848 Mexican Cession of California, Nevada, Utah, and much of present-day Colorado and the American Southwest . The California gold rush of 1848–1849 spurred a huge migration of white settlers to the Pacific coast, leading to even more confrontations with Native populations. One of

15375-754: Was adopted on July 4, 1776. The political values of the American Revolution included liberty , inalienable individual rights ; and the sovereignty of the people ; supporting republicanism and rejecting monarchy , aristocracy , and all hereditary political power; civic virtue ; and vilification of political corruption . The Founding Fathers of the United States , who included Washington, Jefferson, John Adams , Benjamin Franklin , Alexander Hamilton , John Jay , James Madison , Thomas Paine , and many others, were inspired by Greco-Roman , Renaissance , and Enlightenment philosophies and ideas. The Articles of Confederation were ratified in 1781 and established

15500-565: Was elected the country's first president under the Constitution, and the Bill of Rights was adopted in 1791 to allay skeptics' concerns about the power of the more centralized government. His resignation as commander-in-chief after the Revolutionary War and his later refusal to run for a third term as the country's first president established a precedent for the supremacy of civil authority in

15625-424: Was the highest in the world, constituting over 25% of the global economy or 15% at purchasing power parity (PPP). From 1983 to 2008, U.S. real compounded annual GDP growth was 3.3%, compared to a 2.3% weighted average for the rest of the G7 . The country ranks first in the world by nominal GDP , second when adjusted for purchasing power parities (PPP), and ninth by PPP-adjusted GDP per capita . It possesses

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