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Three sigma rule

Prediction interval (on the y-axis) given from the standard score (on the x-axis). The y-axis is logarithmically scaled (but the values on it are not modified).

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively. In mathematical notation, these facts can be expressed as follows, where X is an observation from a normally distributed random variable, μ is the mean of the distribution, and σ is its standard deviation:

In the empirical sciences the so-called three-sigma rule of thumb expresses a conventional heuristic that "nearly all" values are taken to lie within three standard deviations of the mean, i.e. that it is empirically useful to treat 99.7% probability as "near certainty".[1] The usefulness of this heuristic of course depends significantly on the question under consideration, and there are other conventions, e.g. in the social sciences a result may be considered "significant" if its confidence level is of the order of a two-sigma effect (95%), while in particle physics, there is a convention of a five-sigma effect (99.99994% confidence) being required to qualify as a "discovery".

The "three sigma rule of thumb" is related to a result also known as the three-sigma rule, which states that even for non-normally distributed variables, at least 88.8% of cases should fall within properly-calculated three-sigma intervals. It follows from Chebyshev's Inequality. For unimodal distributions the probability of being within the interval is at least 95%. There may be certain assumptions for a distribution that force this probability to be at least 98%.[2]

Cumulative distribution function
Diagram showing the cumulative distribution function for the normal distribution with mean (µ) 0 and variance (σ2 ) 1.

These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution.

The prediction interval for any standard score z corresponds numerically to (1−(1−Φ(z))·2).

For example, Φ(2) ≈ 0.9772, or Pr(X ≤ μ + 2σ) ≈ 0.9772, corresponding to a prediction interval of (1 − (1 − 0.97725)·2) = 0.9545 = 95.45%. Note that this is not a symmetrical interval – this is merely the probability that an observation is less than μ + 2σ. To compute the probability that an observation is within two standard deviations of the mean (small differences due to rounding):

This is related to confidence interval as used in statistics: X ¯ ± 2 σ n {\displaystyle {\bar {X}}\pm 2{\frac {\sigma }{\sqrt {n}}}} is approximately a 95% confidence interval when X ¯ {\displaystyle {\bar {X}}} is the average of a sample of size n {\displaystyle n} .

Normality tests

The "68–95–99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. It is also as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal.

To pass from a sample to a number of standard deviations, one first computes the deviation, either the error or residual depending on whether one knows the population mean or only estimates it. The next step is standardizing (dividing by the population standard deviation), if the population parameters are known, or studentizing (dividing by an estimate of the standard deviation), if the parameters are unknown and only estimated.

To use as a test for outliers or a normality test, one computes the size of deviations in terms of standard deviations, and compares this to expected frequency. Given a sample set, one can compute the studentized residuals and compare these to the expected frequency: points that fall more than 3 standard deviations from the norm are likely outliers (unless the sample size is significantly large, by which point one expects a sample this extreme), and if there are many points more than 3 standard deviations from the norm, one likely has reason to question the assumed normality of the distribution. This holds ever more strongly for moves of 4 or more standard deviations.

One can compute more precisely, approximating the number of extreme moves of a given magnitude or greater by a Poisson distribution, but simply, if one has multiple 4 standard deviation moves in a sample of size 1,000, one has strong reason to consider these outliers or question the assumed normality of the distribution.

For example, a 6σ event corresponds to a chance of about two parts per billion. For illustration, if events are taken to occur daily, this would correspond to an event expected every 1.4 million years. This gives a simple normality test: if one witnesses a 6σ in daily data and significantly fewer than 1 million years have passed, then a normal distribution most likely does not provide a good model for the magnitude or frequency of large deviations in this respect.

In The Black Swan, Nassim Nicholas Taleb gives the example of risk models according to which the Black Monday crash would correspond to a 36-σ event: the occurrence of such an event should instantly suggest that the model is flawed, i.e. that the process under consideration is not satisfactorily modelled by a normal distribution. Refined models should then be considered, e.g. by the introduction of stochastic volatility. In such discussions it is important to be aware of problem of the gambler's fallacy, which states that a single observation of a rare event does not contradict that the event is in fact rare. It is the observation of a plurality of purportedly rare events that increasingly undermines the hypothesis that they are rare, i.e. the validity of the assumed model. A proper modelling of this process of gradual loss of confidence in a hypothesis would involve the designation of prior probability not just to the hypothesis itself but to all possible alternative hypotheses. For this reason, statistical hypothesis testing works not so much by confirming a hypothesis considered to be likely, but by refuting hypotheses considered unlikely.

Table of numerical values

Because of the exponential tails of the normal distribution, odds of higher deviations decrease very quickly. From the rules for normally distributed data for a daily event:

Range Expected fraction of population inside range Approximate expected frequency outside range Approximate frequency for daily event
μ ± 0.5σ 0.382924922548026 2 in 3 Four times a week
μ ± σ 0.682689492137086 1 in 3 Twice a week
μ ± 1.5σ 0.866385597462284 1 in 7 Weekly
μ ± 2σ 0.954499736103642 1 in 22 Every three weeks
μ ± 2.5σ 0.987580669348448 1 in 81 Quarterly
μ ± 3σ 0.997300203936740 1 in 370 Yearly
μ ± 3.5σ 0.999534741841929 1 in 2149 Every six years
μ ± 4σ 0.999936657516334 1 in 15787 Every 43 years (twice in a lifetime)
μ ± 4.5σ 0.999993204653751 1 in 147160 Every 403 years (once in the modern era)
μ ± 0.999999426696856 1 in 1744278 Every 4776 years (once in recorded history)
μ ± 5.5σ 0.999999962020875 1 in 26330254 Every 72090 years (thrice in history of modern humankind)
μ ± 6σ 0.999999998026825 1 in 506797346 Every 1.38 million years (twice in history of humankind)
μ ± 6.5σ 0.999999999919680 1 in 12450197393 Every 34 million years (halfway since the extinction of dinosaurs)
μ ± 7σ 0.999999999997440 1 in 390682215445 Every 1.07 billion years (a quarter of Earth's history)
μ ± xσ erf ( x 2 ) {\displaystyle \operatorname {erf} \left({\frac {x}{\sqrt {2}}}\right)} 1 in 1 1 erf ( x 2 ) {\displaystyle {\tfrac {1}{1-\operatorname {erf} \left({\frac {x}{\sqrt {2}}}\right)}}} Every 1 1 erf ( x 2 ) {\displaystyle {\tfrac {1}{1-\operatorname {erf} \left({\frac {x}{\sqrt {2}}}\right)}}} days
See also
  1. this usage of "three-sigma rule" entered common usage in the 2000s, e.g. cited in Schaum's Outline of Business Statistics. McGraw Hill Professional. 2003. p. 359, and in Grafarend, Erik W. (2006). Linear and Nonlinear Models: Fixed Effects, Random Effects, and Mixed Models. Walter de Gruyter. p. 553.
  2. See:
External links
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Fermi's interaction


β − decay in an atomic nucleus (the accompanying antineutrino is omitted). The inset shows beta decay of a free neutron. In both processes, the intermediate emission of a virtual W − boson (which then decays to electron and antineutrino) is not shown. In particle physics , Fermi's interaction (also the Fermi theory of beta decay ) is an explanation of the beta decay , proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting with one another (at one vertex of the associated Feynman diagram ). This interaction explains beta decay of a neutron by direct coupling of a neutron with an electron , a neutrino (later determined to be an antineutrino ) and a proton . Fermi first introduced this coupling in his description of beta decay in 1933. The Fermi interaction was the precursor to the theory for the weak interaction where the interaction between the proton–neutron and electron–antineutrino is mediated by a virtual W boson . History of initial rejection and later publication Fermi ...more...

Beer–Lambert law


A demonstration of the Beer–Lambert law: green laser light in a solution of Rhodamine 6B . The beam radiant power becomes weaker as it passes through solution The Beer–Lambert law , also known as Beer's law , the Lambert–Beer law , or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics , for photons , neutrons or rarefied gases. In mathematical physics , this law arises as a solution of the BGK equation . History The law was discovered by Pierre Bouguer before 1729. It is often attributed to Johann Heinrich Lambert , who cited Bouguer's Essai d'optique sur la gradation de la lumière (Claude Jombert, Paris, 1729)—and even quoted from it—in his Photometria in 1760. Lambert's law stated that absorbance of a material sample is directly proportional to its thickness (path length). Much later, August Beer discovere ...more...

Leibniz integral rule


In calculus , Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz , states that for an integral of the form where − ∞ a ( x ) , b ( x ) ∞ {\displaystyle -\infty , the derivative of this integral is expressible as where the partial derivative indicates that inside the integral, only the variation of f(x, t) with x is considered in taking the derivative. Notice that if a ( x ) {\displaystyle a(x)} and b ( x ) {\displaystyle b(x)} are constants rather than functions of x {\displaystyle x} , we have a special case of Leibniz's rule: Thus under certain conditions, one may interchange the integral and partial differential operators . This important result is particularly useful in the differentiation of integral transforms . An example of such is the moment generating function in probability theory, a variation of the Laplace transform , which can be differentiated to generate the moments of a random variable . Whether Leibniz's integral rule applies is essentially a question ...more...

Conditional independence


In probability theory , two events R and B are conditionally independent given a third event Y precisely if the occurrence of R and the occurrence of B are independent events in their conditional probability distribution given Y. In other words, R and B are conditionally independent given Y if and only if, given knowledge that Y occurs, knowledge of whether R occurs provides no information on the likelihood of B occurring, and knowledge of whether B occurs provides no information on the likelihood of R occurring. Formal definition These are two examples illustrating conditional independence . Each cell represents a possible outcome. The events R, B and Y are represented by the areas shaded red, blue and yellow respectively. The overlap between the events R and B is shaded purple. The probabilities of these events are shaded areas with respect to the total area. In both examples R and B are conditionally independent given Y because: Pr ( R ∩ B ∣ Y ) = Pr ( R ∣ Y ) Pr ( B ∣ Y ) {\displaystyle \Pr(R\cap B\mid Y) ...more...



Quaternion multiplication × 1 i j k 1 1 i j k i i −1 k −j j j −k −1 i k k j −i −1 In mathematics , the quaternions are a number system that extends the complex numbers . They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space . A feature of quaternions is that multiplication of two quaternions is noncommutative . Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors . Quaternions are generally represented in the form: where a, b, c, and d are real numbers, and i , j , and k are the fundamental quaternion units. Quaternions find uses in both theoretical and applied mathematics , in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics , computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as Euler angles and ro ...more...

Ricci calculus


In mathematics , Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields . It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus ), developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. Jan Arnoldus Schouten developed the modern notation and formalism for this mathematical framework, and made contributions to the theory, during its applications to general relativity and differential geometry in the early twentieth century. A component of a tensor is a real number which is used as a coefficient of a basis element for the tensor space. The tensor is the sum of its components multiplied by their basis elements. Tensors and tensor fields can be expressed in terms of their components, and operations on tensors and tensor fields can be expressed in terms of operations on their components. The description of te ...more...

Heath–Jarrow–Morton framework


The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curve – instantaneous forward rate curve in particular (as opposed to simple forward rates ). When the volatility and drift of the instantaneous forward rate are assumed to be deterministic , this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example. The HJM framework originates from the work of David Heath , Robert A. Jarrow , and Andrew Morton in the late 1980s, especially Bond pricing and the term structure of interest rates: a new methodology (1987) – working paper, Cornell University , and Bond pricing and the term structure of interest rates: a new methodology (1989) – working paper (revised ed.), Cornell University. It has its critics, however, with Paul Wilmott describing it as "...actually just a big rug for [mistakes] to be swept under". Framework The key to these techniques is ...more...

Murray State University


Murray State University ( MSU ) is a four-year public university located in Murray, Kentucky , United States. With about 10,500 students, it has been recognized by U.S. News & World Report ' s "Best Colleges" as one of the top regional universities in the U.S. for 26 straight years. It has consistently been one of the top-ranked public regional universities in Kentucky (out of 6) but it is currently ranked 35th among regional universities in the South by US News. In addition to the main campus, Murray State operates extended campuses offering upper level and graduate courses in Paducah , Hopkinsville , Madisonville , and Henderson . History The history of Murray State University can be traced to the passage of Senate Bill 14 by the General Assembly of the Commonwealth of Kentucky, which created two normal schools to address the growing demand for professional teachers. One would be in the western part of the state, which caused many cities and towns to bid for the new normal school. Rainey T. Wells spok ...more...

University of South Carolina


The University of South Carolina (also referred to as USC , SC , South Carolina , or simply Carolina ) is a public , co-educational research university in Columbia, South Carolina , United States, with seven satellite campuses. Its campus covers over 359 acres (145 ha) in downtown Columbia not far from the South Carolina State House . The University is categorized by the Carnegie Foundation for the Advancement of Teaching as having "highest research activity." It has been ranked as an "up-and-coming" university by U.S. News & World Report , and its undergraduate and graduate International Business programs have ranked among the top three programs in the nation for over a decade. It also houses the largest collection of Robert Burns and Scottish literature materials outside Scotland, and the world's largest Ernest Hemingway collection. Founded in 1801 as South Carolina College , South Carolina is the flagship institution of the University of South Carolina System and offers more than 350 programs of s ...more...

Truman State University


Truman State University ( TSU or Truman ) is a public liberal arts and sciences university located in Kirksville, Missouri , United States. It is a member of the Council of Public Liberal Arts Colleges . It had 6,379 enrolled students in the fall of 2015, with 6,039 undergraduate and 340 postgraduate students, pursuing degrees in 48 undergraduate, and eight graduate programs. The university is named after U.S. President Harry Truman , the only president born in Missouri. Until 1996, the school was known as Northeast Missouri State University , but the Board of Trustees voted to change the school's name to better reflect its statewide mission. In the 2016 U.S. News & World Report College Rankings, Truman placed eighth in the Midwest among regional universities. Truman State is the only public institution in Missouri that is officially designated to pursue highly selective admissions standards. History North Entrance on East Normal Street Truman State University was founded in 1867 by Joseph Baldwin as ...more...

Latent semantic analysis


Latent semantic analysis ( LSA ) is a technique in natural language processing , in particular distributional semantics , of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis ). A matrix containing word counts per paragraph (rows represent unique words and columns represent each paragraph) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Words are then compared by taking the cosine of the angle between the two vectors (or the dot product between the normalizations of the two vectors) formed by any two rows. Values close to 1 represent very similar words while values close to 0 represent very dissimilar words. An information retrieval technique us ...more...

David Spade


David Wayne Spade (born July 22, 1964) is an American actor, stand-up comedian, writer, and television personality. He rose to fame in the 1990s as a cast member on Saturday Night Live , then began a successful acting career in both film and television. He also starred and co-starred in the films Tommy Boy , Black Sheep , Joe Dirt , Joe Dirt 2: Beautiful Loser , Grown Ups , and Grown Ups 2 , among others. He has also been part of an ensemble cast of two long-running sitcoms: Just Shoot Me! (1997–2003) and Rules of Engagement (2007–2013). He also starred as C. J. Barnes in the sitcom 8 Simple Rules (2004–2005). In animation, he voiced Kuzco in the 2000 film The Emperor's New Groove and its direct-to-video sequel, Kronk's New Groove . His comedic style, in both his stand-up material and acting roles, relies heavily on sarcasm and self-deprecation . Early life Spade was born in Birmingham, Michigan . He is the son of Judith J. (née Meek), a writer and magazine editor, and Wayne M. Spade, a sales representative. ...more...

1992–93 UEFA Cup


The 1992–93 UEFA Cup was won by Juventus , who beat Borussia Dortmund 6–1 in the final aggregate over, a record score for a UEFA Cup final . It was the third victory in the competition for the Italian team (first club to reach this record). Three seasons had now passed since the ban on English clubs in European competitions as a result of the Heysel disaster (1985) had been lifted, and for this campaign the number of English clubs in the competition was increased from one to two. English league runners-up Manchester United were joined by third placed Sheffield Wednesday , though both teams ultimately had a short-lived run in the competition. Ajax were the defending champions, but were eliminated in the quarter-finals by Auxerre . First round Team 1 Agg. Team 2 1st leg 2nd leg Köln 2–3 Celtic 2–0 0–3 Dynamo Moscow 5–3 Rosenborg BK 5–1 0–2 Electroputere Craiova 0–10 Panathinaikos 0–6 0–4 Dynamo Kyiv ( a )3–3 Rapid Wien 1–0 2–3 Copenhagen 10–1 MP 5–0 5–1 Wacker Innsbruck 1–5 Roma 1–4 0–1 Politehnica Timișoara 1– ...more...

American Society for Quality


ASQ registration booth at America's Center in St. Louis for the 2010 meeting on 24 May The American Society for Quality ( ASQ ), formerly the American Society for Quality Control ( ASQC ), is a knowledge-based global community of quality professionals, with nearly 80,000 members dedicated to promoting and advancing quality tools, principles, and practices in their workplaces and communities. History ASQC was established in 1946 in Milwaukee , Wisconsin , as a way for quality experts and manufacturers to sustain quality-improvement techniques used during World War II . The organisation changed its name from "American Society for Quality Control" to "American Society for Quality" in 1997. Today, ASQ is a global organization with members in more than 150 countries. ASQ has service centers in Mexico, China and India, and has established strategic alliances with many organizations in countries like Brazil and the United Arab Emirates to promote ASQ products and training. Quality ASQ provides its members with certi ...more...



Example distribution with non-zero (positive) skewness. These data are from experiments on wheat grass growth. In probability theory and statistics , skewness is a measure of the asymmetry of the probability distribution of a real -valued random variable about its mean. The skewness value can be positive or negative, or undefined. The qualitative interpretation of the skew is complicated and unintuitive. Skew does not refer to the direction the curve appears to be leaning; in fact, the opposite is true. For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side – it does not distinguish these two kinds of shape. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this ...more...



The J- integral represents a way to calculate the strain energy release rate , or work ( energy ) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by Cherepanov and in 1968 by Jim Rice independently, who showed that an energetic contour path integral (called J) was independent of the path around a crack . Later, experimental methods were developed, which allowed measurement of critical fracture properties using laboratory-scale specimens for materials in which sample sizes are too small and for which the assumptions of Linear Elastic Fracture Mechanics (LEFM) do not hold, and to infer a critical value of fracture energy J. The quantity J defines the point at which large-scale plastic yielding during propagation takes place under mode one loading. The J-integral is equal to the strain energy release rate for a crack in a body subjected to monotonic loading. This is generally true, under quasistatic conditions, only for linear elastic materials. For ...more...

Stokes' theorem


In vector calculus , and more generally differential geometry , Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem ) is a statement about the integration of differential forms on manifolds , which both simplifies and generalizes several theorems from vector calculus . Stokes' theorem says that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω , i.e., Stokes' theorem was formulated in its modern form by Élie Cartan following earlier work on the generalization of the theorems of vector calculus by Vito Volterra , Édouard Goursat , and Henri Poincaré . This modern form of Stokes' theorem is a vast generalization of a classical result . Lord Kelvin communicated it to George Stokes in a letter dated July 2, 1850. Stokes set the theorem as a question on the 1854 Smith's Prize exam, which led to the result bearing his name, even though it was actually first publish ...more...

List of Phi Sigma Kappa chapters


The complete Chapter and Colony Roll of Phi Sigma Kappa follows this gallery of historic and newer images. Hover over photos for chapter names and captions. Many of the buildings in the historical photos are still owned by Phi Sig fraternity chapters and their alumni today, having been remodeled and expanded, while others have been replaced: Historical Chapterhouse Images Phi Sigma Kappa's Gamma chapter, at Cornell University, circa 1903. Newly remodeled 2014 ΦΣΚ's founding Alpha chapter, circa 1910. Newly remodeled 2015 ΦΣΚ's Beta Deuteron chapter, at Minnesota, circa 1933. Holds 26 live-ins today ΦΣΚ's Nu chapter, at Lehigh, circa 1948 ΦΣΚ's Epsilon chapter, Sachem Hall, at Yale, 1907 ΦΣΚ Beta chap Union ΦΣΚ's Delta chapter, West Virginia, 1910. Since replaced with a larger home ΦΣΚ's Delta chapter, at West Virginia, circa 1941 ΦΣΚ's Eta chapter, at Maryland, circa 1954 ΦΣΚ's Chi chapter, at Williams, previous house, prior to 1947 ΦΣΚ's Chi chapter, at Williams, circa 1947 ΦΣΚ's Omicron chapter, at MIT, (fo ...more...

Alpha Sigma Alpha


Alpha Sigma Alpha ( ΑΣΑ ) is a United States National Panhellenic sorority founded on November 15, 1901 at the Virginia State Female Normal School (later known as Longwood College and now known as Longwood University ) in Farmville , Virginia . The purpose of the association is to cultivate the relationship among members. Alpha Sigma Alpha promotes high ideal and standards for its members throughout their lives by emphasizing balance among four aims of intellectual, physical, social and spiritual development. With the effort of each member, Alpha Sigma Alpha became a full member of National Panhellenic Conference in 1951. The insignia of Alpha Sigma Alpha are the star, crown, palm tree and phoenix. The star represents the aspirations of Alpha Sigma Alphas to live up to the values of the Sorority. The crown represents leadership attained and the name of recognition given to our alumnae. The palm tree represents an emblem of sturdy development. The phoenix, the central symbol in our coat-of-arms, openly represe ...more...

Mathematics of general relativity


The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying and formulating Albert Einstein 's theory of general relativity . The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime . This article is a general description of the mathematics of general relativity. Tensors The principle of general covariance states that the laws of physics should take the same mathematical form in all reference frames and was one of the central principles in the development of general relativity. The term 'general covariance' was used in the early formulation of general relativity, but is now referred to by many as diffeomorphism covariance . Although diffeomorphism covariance is not the defining feature of general relativity , and controversies remain regarding its present status in general relativity, the invariance property of physical laws implied in the principle coupled with the fact ...more...



Advanced Photo System type-C ( APS-C ) is an image sensor format approximately equivalent in size to the Advanced Photo System "classic" negatives of 25.1×16.7 mm, an aspect ratio of 3:2. CCD Sony ICX493AQA 10.14(Gross 10.75) Mpixels APS-C 1.8″ (23.98×16.41 mm) sensor side Sensors approximating these dimensions are used in many digital single-lens reflex cameras (DSLRs), Mirrorless interchangeable-lens cameras (MILCs), and a few large-sensor live-preview digital cameras . APS-C size sensors are also used in a few digital rangefinders . Such sensors exist in many different variants depending on the manufacturer and camera model. All APS-C variants are considerably smaller than 35 mm standard film which measures 36×24 mm. Because of this, devices with APS-C sensors are known as "cropped frame," especially when used in connection with lens mounts that are also used with sensors the size of 35 mm film: only part of the image produced by the lens is captured by the APS-C size sensor. Sensor sizes range from 20.7× ...more...

Clemson University Greek life


Clemson University opened in 1893 as an all-male military college. It was not until seventy years later in 1959 that the first fraternities and sororities arrived on campus. In the 1970s, they became recognized as national fraternities and sororities. The Greek life has now increased to 44 chapters on campus: fraternities and sororities from the National Panhellenic Conference , the North-American Interfraternity Conference , the Multicultural Greek Council, and the National Pan-Hellenic Council . The Greek life office is located in Norris Hall. Of the 22,698 enrolled undergraduate students, 18% of males are involved in fraternities while 32% of females are involved in sororities Affiliated men and women have shown to have a higher GPR than nonaffiliated men and women. Clemson University Greek life is unique because Greeks do not have houses on campus but live in separate residence halls. However many fraternities operate large off-campus houses in or near the North Clemson Neighborhood adjacent to campu ...more...

Quantitative genetics


Quantitative genetics is a branch of population genetics that deals with phenotypes that vary continuously (in characters such as height or mass)—as opposed to discretely identifiable phenotypes and gene-products (such as eye-colour, or the presence of a particular biochemical). Both branches use the frequencies of different alleles of a gene in breeding populations (gamodemes), and combine them with concepts from simple Mendelian inheritance to analyze inheritance patterns across generations and descendant lines. While population genetics can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes summaries only of the underlying genetics. Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods (such as the effect size, the mean and the variance) to link phenotypes (attributes) to genotypes. Some phenotypes may be analyzed either as discrete categories or as con ...more...



Each of the six rows is a different permutation of three distinct balls In mathematics , the notion of permutation relates to the act of arranging all the members of a set into some sequence or order , or if the set is already ordered, rearranging (reordering) its elements, a process called permuting . These differ from combinations , which are selections of some members of a set where order is disregarded. For example, written as tuples , there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics . Permutations occur, in more or less prominent ways, in almost every area of mathematics. T ...more...

Grove City College


Grove City College ( GCC ) is a Christian liberal arts college in Grove City, Pennsylvania , about 50 miles (80 km) north of Pittsburgh . According to the College Bulletin, its stated threefold mission is to provide an excellent education at an affordable price in a thoroughly Christian environment. Former College president Richard Jewell has said, "The two tenets that this school is most about are faith and freedom." The school emphasizes a humanities core curriculum , which endorses the Judeo-Christian Western tradition and the free market . Though loosely associated with the Presbyterian Church , the college is non-denominational . Students are not required to sign a statement of faith , but are required to attend sixteen chapel services per semester. History Founding Founded in 1876 by Isaac C. Ketler , the school was originally chartered as Pine Grove Normal Academy. It had twenty-six students in its first year. In 1884, the trustees of Pine Grove Normal Academy in Grove City amended the academy charte ...more...

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