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*[http://en.wikipedia.org/wiki/19th_century 1894]

*[https://en.wikipedia.org/wiki/19th_century 1894]

==Definition==

==Definition==

*1:  the [[symmetrical]] bell-shaped curve of a [[normal]] [[distribution]]

*1:  the [[symmetrical]] bell-shaped curve of a [[normal]] [[distribution]]

==Description==

==Description==

In [http://en.wikipedia.org/wiki/Probability_theory probability theory], the '''normal''' (or Gaussian) distribution is a very commonly occurring [http://en.wikipedia.org/wiki/Continuous_probability_distribution continuous probability distribution]—a function that tells the probability that an [[observation]] in some context will fall between any two [http://en.wikipedia.org/wiki/Real_number real numbers]. For example, the distribution of income measured on a log scale is normally distributed in some [[contexts]], as is often the distribution of grades on a test administered to many people. Normal distributions are extremely important in [[statistics]] and are often used in the natural and [[social sciences]] for real-valued [http://en.wikipedia.org/wiki/Random_variable random variables] whose distributions are not known.

In [https://en.wikipedia.org/wiki/Probability_theory probability theory], the '''normal''' (or Gaussian) distribution is a very commonly occurring [https://en.wikipedia.org/wiki/Continuous_probability_distribution continuous probability distribution]—a function that tells the probability that an [[observation]] in some context will fall between any two [https://en.wikipedia.org/wiki/Real_number real numbers]. For example, the distribution of income measured on a log scale is normally distributed in some [[contexts]], as is often the distribution of grades on a test administered to many people. Normal distributions are extremely important in [[statistics]] and are often used in the natural and [[social sciences]] for real-valued [https://en.wikipedia.org/wiki/Random_variable random variables] whose distributions are not known.

The '''normal distribution''' is immensely useful because of the [http://en.wikipedia.org/wiki/Central_limit_theorem central limit theorem], which states that, under mild conditions, the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution: physical [[quantities]] that are [[expected]] to be the sum of many independent processes (such as measurement errors) often have a distribution very close to the normal. Moreover, many results and [[methods]] (such as [http://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

The '''normal distribution''' is immensely useful because of the [https://en.wikipedia.org/wiki/Central_limit_theorem central limit theorem], which states that, under mild conditions, the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution: physical [[quantities]] that are [[expected]] to be the sum of many independent processes (such as measurement errors) often have a distribution very close to the normal. Moreover, many results and [[methods]] (such as [https://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

The Gaussian distribution is sometimes informally called the '''bell curve'''. However, many other distributions are bell-shaped (such as Cauchy's, Student's, and logistic). The terms [http://en.wikipedia.org/wiki/Gaussian_function Gaussian function] and '''Gaussian bell curve''' are also [[ambiguous]] because they sometimes refer to multiples of the normal distribution that cannot be directly [[interpreted]] in terms of [[probabilities]].[http://en.wikipedia.org/wiki/Normal_distribution]

The Gaussian distribution is sometimes informally called the '''bell curve'''. However, many other distributions are bell-shaped (such as Cauchy's, Student's, and logistic). The terms [https://en.wikipedia.org/wiki/Gaussian_function Gaussian function] and '''Gaussian bell curve''' are also [[ambiguous]] because they sometimes refer to multiples of the normal distribution that cannot be directly [[interpreted]] in terms of [[probabilities]].[https://en.wikipedia.org/wiki/Normal_distribution]

==Bell Curve Book==

==Bell Curve Book==

''The Bell Curve: Intelligence and Class Structure in American Life'' is a 1994 book by American psychologist [http://en.wikipedia.org/wiki/Richard_J._Herrnstein Richard J. Herrnstein] (who died before the book was released) and American political scientist [http://en.wikipedia.org/wiki/Charles_Murray_(author) Charles Murray]. Its central argument is that human [[intelligence]] is substantially influenced by both inherited and environmental factors and is a better predictor of many personal [[dynamics]], including [[financial]] income, job performance, [[chance]] of unwanted pregnancy, and involvement in [[crime]] than are an individual's parental socioeconomic [[status]], or [[education]] level. The book also argues that those with high intelligence, the "cognitive elite", are becoming [[separated]] from those of average and below-average intelligence, and that this is a [[dangerous]] social trend with the [[United States]] moving toward a more divided [[society]] similar to that in [http://en.wikipedia.org/wiki/Latin_America Latin America].

''The Bell Curve: Intelligence and Class Structure in American Life'' is a 1994 book by American psychologist [https://en.wikipedia.org/wiki/Richard_J._Herrnstein Richard J. Herrnstein] (who died before the book was released) and American political scientist [https://en.wikipedia.org/wiki/Charles_Murray_(author) Charles Murray]. Its central argument is that human [[intelligence]] is substantially influenced by both inherited and environmental factors and is a better predictor of many personal [[dynamics]], including [[financial]] income, job performance, [[chance]] of unwanted pregnancy, and involvement in [[crime]] than are an individual's parental socioeconomic [[status]], or [[education]] level. The book also argues that those with high intelligence, the "cognitive elite", are becoming [[separated]] from those of average and below-average intelligence, and that this is a [[dangerous]] social trend with the [[United States]] moving toward a more divided [[society]] similar to that in [https://en.wikipedia.org/wiki/Latin_America Latin America].

The book was [[controversial]], especially where the [[authors]] wrote about racial [[differences]] in intelligence and discussed the implications of those differences. The authors were reported throughout the popular press as arguing that these IQ differences are [[genetic]]. They wrote in chapter 13: "It seems highly likely to us that both genes and the environment have something to do with racial differences." The introduction to the chapter more cautiously states, "The [[debate]] about whether and how much genes and environment have to do with ethnic [[differences]] remains unresolved."

The book was [[controversial]], especially where the [[authors]] wrote about racial [[differences]] in intelligence and discussed the implications of those differences. The authors were reported throughout the popular press as arguing that these IQ differences are [[genetic]]. They wrote in chapter 13: "It seems highly likely to us that both genes and the environment have something to do with racial differences." The introduction to the chapter more cautiously states, "The [[debate]] about whether and how much genes and environment have to do with ethnic [[differences]] remains unresolved."

The book's title comes from the bell-shaped normal distribution of [http://en.wikipedia.org/wiki/Intelligence_quotient intelligence quotient] (IQ) scores in a [[population]].

The book's title comes from the bell-shaped normal distribution of [https://en.wikipedia.org/wiki/Intelligence_quotient intelligence quotient] (IQ) scores in a [[population]].

Shortly after publication, many people rallied both in [[criticism]] and defense of the book. A number of critical [[texts]] were written in response to the [[book]].

Shortly after publication, many people rallied both in [[criticism]] and defense of the book. A number of critical [[texts]] were written in response to the [[book]].