In mathematics and statistics, the arithmetic mean, arithmetic average, or just the mean or average is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic.
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
The Flynn effect is the substantial and long-sustained increase in both fluid and crystallized intelligence test scores that were measured in many parts of the world over the 20th century, named after researcher James Flynn (1934–2020). When intelligence quotient (IQ) tests are initially standardized using a sample of test-takers, by convention the average of the test results is set to 100 and their standard deviation is set to 15 or 16 IQ points. When IQ tests are revised, they are again standardized using a new sample of test-takers, usually born more recently than the first; the average result is set to 100. When the new test subjects take the older tests, in almost every case their average scores are significantly above 100.
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of positive real numbers by using the product of their values. The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers a1, a2, ..., an, the geometric mean is defined as
A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. There are several kinds of means in mathematics, especially in statistics. Each attempts to summarize or typify 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.
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops. Primitive recursive functions form a strict subset of those general recursive functions that are also total functions.
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not.
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling.
In ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean average of the numbers 2, 3, 4, 7, and 9 is 5. Depending on the context, the most representative statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, mode or geometric mean. For example, the average personal income is often given as the median – the number below which are 50% of personal incomes and above which are 50% of personal incomes – because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency and specify which type of measure of average is being used.
In mathematics, the root mean square of a set of numbers is the square root of the set's mean square. Given a set , its RMS is denoted as either or . The RMS is also known as the quadratic mean, a special case of the generalized mean. The RMS of a continuous function is denoted and can be defined in terms of an integral of the square of the function.
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition.
In medicine and health-related fields, a reference range or reference interval is the range or the interval of values that is deemed normal for a physiological measurement in healthy persons. It is a basis for comparison for a physician or other health professional to interpret a set of test results for a particular patient. Some important reference ranges in medicine are reference ranges for blood tests and reference ranges for urine tests.
George Stephen Boolos was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
In the theory of computation, the Sudan function is an example of a function that is recursive, but not primitive recursive. This is also true of the better-known Ackermann function.
The Hispanic paradox is an epidemiological finding that Hispanic Americans tend to have health outcomes that "paradoxically" are comparable to, or in some cases better than, those of their U.S. non-Hispanic White counterparts, even though Hispanics have lower average income and education, higher rates of disability, as well as a higher incidence of various cardiovascular risk factors and metabolic diseases.
Peridynamics is a non-local formulation of continuum mechanics that is oriented toward deformations with discontinuities, especially fractures. Originally, bond-based peridynamic has been introduced, wherein, internal interaction forces between a material point and all the other ones with which it can interact, are modeled as a central forces field. This type of force fields can be imagined as a mesh of bonds connecting each point of the body with every other interacting point within a certain distance which depends on material property, called peridynamic horizon. Later, to overcome bond-based framework limitations for the material Poisson’s ratio, state-base peridynamics, has been formulated. Its characteristic feature is that the force exchanged between a point and another one is influenced by the deformation state of all other bonds relative to its interaction zone.
In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary or complex number.
In social psychology, illusory superiority is a cognitive bias wherein people overestimate their own qualities and abilities compared to others. Illusory superiority is one of many positive illusions, relating to the self, that are evident in the study of intelligence, the effective performance of tasks and tests, and the possession of desirable personal characteristics and personality traits. Overestimation of abilities compared to an objective measure is known as the overconfidence effect.
In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3).
Type theory with records is a formal semantics representation framework, using records to express type theory types. It has been used in natural language processing, principally computational semantics and dialogue systems.
