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Median Average
The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a 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 mean (often simply described as the "average") is that it is not 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 listed in order from smallest to greatest. If the data set has an odd numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finding The Median
Find, FIND or Finding may refer to: Computing * find (Unix), a command on UNIX platforms * find (Windows), a command on DOS/Windows platforms Books * ''The Find'' (2010), by Kathy Page * ''The Find'' (2014), by William Hope Hodgson Film and television * "The Find", an episode of '' Beyond Belief: Fact or Fiction'' * "The Find", an episode of reality TV show '' The Curse of Oak Island'' Music * ''Find'' (Hidden in Plain View EP), 2001 * ''Find'' (SS501 EP) * '' The Find'', a 2005 hip hop album by Ohmega Watts People * Áed Find (died 778), king of Dál Riata (modern-day Scotland) * Caittil Find, Norse-Gaelic warrior contingent leader * Cumméne Find (died 669), seventh abbot of Iona, Scotland Other uses * Find, in archaeology * Finding (jewelcrafting), jewellery components * Meteorite find, a found meteorite not observed to have fallen * Foundation for Innovative New Diagnostics, a not-for-profit organisation * Facial Images National Database See also * Discovery (observa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.. There are several common ways of formalizing weak orderings, that are different from each other but Cryptomorphism, cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partition of a set, partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases anot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
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] |
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] |
Multiset
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the ''multiplicity'' of that element in the multiset. As a consequence, an infinite number of multisets exist that contain only elements and , but vary in the multiplicities of their elements: * The set contains only elements and , each having multiplicity 1 when is seen as a multiset. * In the multiset , the element has multiplicity 2, and has multiplicity 1. * In the multiset , and both have multiplicity 3. These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to ''tuples'', the order in which elements are listed does not matter in discriminating multisets, so and denote the same multiset. To distinguish between sets and multisets, a notat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust statistics, robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, wh ... [...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] |
Percentile
In statistics, a ''k''-th percentile, also known as percentile score or centile, is a score (e.g., a data point) a given percentage ''k'' of all scores in its frequency distribution exists ("exclusive" definition) or a score a given percentage of the all scores exists ("inclusive" definition); i.e. a score in the ''k''-th percentile would be above approximately ''k''% of all scores in its set. For example, the 97th percentile of data is a data point below which 97% of all data points exist (by the exclusive definition). Percentiles depends on how scores are arranged. Percentiles are a type of quantiles, obtained adopting a subdivision into 100 groups. The 25th percentile is also known as the first '' quartile'' (''Q''1), the 50th percentile as the ''median'' or second quartile (''Q''2), and the 75th percentile as the third quartile (''Q''3). For example, the 50th percentile (median) is the score (or , depending on the definition) which 50% of the scores in the distribution are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decile
In descriptive statistics, a decile is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 1/10 of the sample or population. A decile is one possible form of a quantile; others include the quartile and percentile.. A decile rank arranges the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points. Special usage: The decile mean A moderately robust measure of central tendency - known as the decile mean - can be computed by making use of a sample's deciles D_ to D_ (D_ = 10th percentile, D_ = 20th percentile and so on). It is calculated as follows: : DM = \frac Apart from serving as an alternative for the mean and the truncated mean, it also forms the basis for robust measures of skewness and kurtosis In probability theory and statistics, kurtosis (from , ''kyrtos'' or ''kurtos'', meaning "curved, arching") refers to the degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartile
In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three quartiles, resulting in four data divisions, are as follows: * The first quartile (''Q''1) is defined as the 25th percentile where lowest 25% data is below this point. It is also known as the ''lower'' quartile. * The second quartile (''Q''2) is the median of a data set; thus 50% of the data lies below this point. * The third quartile (''Q''3) is the 75th percentile where lowest 75% data is below this point. It is known as the ''upper'' quartile, as 75% of the data lies below this point. Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Location Parameter
In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter x_0, which determines the "location" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways: * either as having a probability density function or probability mass function f(x - x_0); or * having a cumulative distribution function F(x - x_0); or * being defined as resulting from the random variable transformation x_0 + X, where X is a random variable with a certain, possibly unknown, distribution. See also . A direct example of a location parameter is the parameter \mu of the normal distribution. To see this, note that the probability density function f(x , \mu, \sigma) of a normal distribution \mathcal(\mu,\sigma^2) can have the parameter \mu factored out and be written as: : g(x' = x - \mu , \sigma) = \frac \exp\left(-\f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
