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Mean Sea Level
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 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, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Tendency
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications in the Social Sciences, p.2 Colloquially, measures of central tendency are often called '' averages.'' The term ''central tendency'' dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."Upton, G.; Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP (entry for "central tendency")Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP for International Statistical Institute. (entry for "cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean 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 numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
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, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. 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 in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Consider the two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mid-range
In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the arithmetic mean of the maximum and minimum values of the data set: :M=\frac. The mid-range is closely related to the range, a measure of statistical dispersion defined as the difference between maximum and minimum values. The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values. The mid-range is rarely used in practical statistical analysis, as it lacks efficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacks robustness, as outliers change it significantly. Indeed, for many distributions it is one of the least efficient and least robust statistics. However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as an L-estima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode (statistics)
In statistics, the mode is the value that appears most often in a set of data values. If is a discrete random variable, the mode is the value at which the probability mass function takes its maximum value (i.e., ). In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population (statistics), population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions. The mode is not necessarily unique in a given discrete distribution since the probability mass function may take the same maximum value at several points , , etc. The most extreme case occurs in Uniform distribution (discrete), uniform distributions, where all values occur equally frequently. A mode of a continuous probability distribution is often conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the Arithmetic mean, mean (often simply described as the "average") is that it is not Skewness, skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics. Median is a 2-quantile; it is the value that partitions a set into two equal parts. Finite set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are liste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descriptive Statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visualisation Mode Median Mean
Visualization or visualisation may refer to: * Visualization (graphics), the physical or imagining creation of images, diagrams, or animations to communicate a message * Data and information visualization, the practice of creating visual representations of complex data and information * Music visualization, animated imagery based on a piece of music * Mental image, the experience of images without the relevant external stimuli * "Visualization", a song by Blank Banshee on the 2012 album '' Blank Banshee 0'' See also * Creative visualization (other) * Visualizer (other) * * * * Graphics * List of graphical methods, various forms of visualization * Guided imagery, a mind-body intervention by a trained practitioner * Illustration, a decoration, interpretation or visual explanation of a text, concept or process * Image, an artifact that depicts visual perception, such as a photograph or other picture * Infographics Infographics (a clipped compound of "in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Mean Median Mode
Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field: To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and the arts. General usage Comparison is a natural activity, which even animals engage in when decidin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonnegative
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero. In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate binary aspects of mathematical or scientific objects, such as odd and even ( sign of a permutation), sense of orientation or rotation ( cw/ccw), one sided limits, and other concepts described in below. Sign of a number Numbers from various number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed
In kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a non-negative scalar quantity. Introduction of the speed/velocity terminology by Prof. Tait, in 1882. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of ''velocity'' (a vector), which indicates additionally the direction of motion. Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second (m/s), but the most common unit of speed in everyday usage is the kilometre per hour (km/h) or, in the US and the UK, miles per hour (mph). For air and marine travel, the knot is commonly used. The fastest possible speed at wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
