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Arithmetic mean

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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 contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric and harmonic.

AverageAverageNumber taken as representative of a list of numbersIn mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position. In mathematics, it most commonly refers to the arithmetic mean, but may also refer to other measures such as other types of mean, the median, or the mode.StatisticsStatisticsStudy of collection and analysis of dataThe normal distribution, a very common probability density, is used extensively in inferential statistics.Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.Statistics (from German: Statistik, orig.Geometric meanGeometric meanIn mathematics, the geometric mean (also known as the mean proportional) is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of ⁠ n {\displaystyle n} ⁠ numbers is the nth root of their product, i.e., for a collection of numbers a1, a2, ..., an, the geometric mean is defined as a 1 a 2 ⋯ a n t n .Harmonic meanHarmonic meanIn mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is sometimes used for ratios and rates such as speeds, and is normally used for positive arguments only. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x)=1x{\displaystyle f(x)={\frac {1}{x}}}.MathematicsMathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.Observational studyObservational studyIn fields such as epidemiology, social sciences, psychology and statistics, an observational study draws conclusions without controlling the independent variable due to ethical or practical limitations. One common example studies the effect of a treatment, where the researcher does not assign subjects to treatment or control group.ExperimentExperimentAn experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies.HistoryHistoryHistory is the systematic study of the past, focusing primarily on the human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some theorists categorize history as a social science, while others see it as part of the humanities or consider it a hybrid discipline.AnthropologyAnthropologyAnthropology is the scientific study of humanity that crosses biology and sociology, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including archaic humans. Social anthropology studies patterns of behavior, while cultural anthropology studies cultural meaning, including norms and values. The term sociocultural anthropology is commonly used today.Survey methodologySurvey methodologySurvey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving the number and accuracy of responses to surveys.EconomicsEconomicsSocial science studying goods and servicesEuro coinsEconomics () is a social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyses what is viewed as the basic elements of economies, including individual agents and markets, their interactions, and the outcomes of those interactions.

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