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Grouped Data
Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data. There are two major types of grouping: data binning of a single-dimensional variable, replacing individual numbers by counts in bins; and grouping multi-dimensional variables by some of the dimensions (especially by independent variables), obtaining the distribution of ungrouped dimensions (especially the dependent variables). Example The idea of grouped data can be illustrated by considering the following raw dataset: The above data can be grouped in order to construct a frequency distribution in any of several ways. One method is to use intervals as a basis. The smallest value in the above data is 8 and the largest is 34. The interval from 8 to 34 is broken up into smaller subintervals (called ''class intervals''). For each class interval, the number of data item ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data
Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data are usually organized into structures such as tables that provide additional context and meaning, and may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data are commonly used in scientific research, economics, and virtually every other form of human organizational activity. Examples of data sets include price indices (such as the consumer price index), unemployment rates, literacy rates, and census data. In this context, data represent the raw facts and figures from which useful information can be extracted. Data are collected using technique ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Mean
The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from the Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales. The sample mean is used as an estimator for the population mean, the average value in the entire population, where the estimate is more likely to be close to the population mean if the sample is large and representative. The reliability of the sample mean is estimated using the standard error, which in turn is calculated using the variance of the sample. If the sample is random, the standard error falls with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization Of Continuous Features
In statistics and machine learning, discretization refers to the process of converting or partitioning continuous attributes, features or variables to discretized or nominal attributes/features/variables/ intervals. This can be useful when creating probability mass functions – formally, in density estimation. It is a form of discretization in general and also of binning, as in making a histogram. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level considered negligible for the modeling purposes at hand. Typically data is discretized into partitions of ''K'' equal lengths/width (equal intervals) or K% of the total data (equal frequencies). Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, which uses mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Distribution
In statistics, the frequency or absolute frequency of an Event (probability theory), event i is the number n_i of times the observation has occurred/been recorded in an experiment or study. These frequencies are often depicted graphically or tabular form. Types The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events. The Empirical probability, relative frequency (or ''empirical probability'') of an event is the absolute frequency Normalizing constant, normalized by the total number of events: : f_i = \frac = \frac. The values of f_i for all events i can be plotted to produce a frequency distribution. In the case when n_i = 0 for certain i, pseudocounts can be added. Depicting frequency distributions A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level Of Measurement
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. Other classifications include those by Mosteller and Tukey, and by Chrisman. Stevens's typology Overview Stevens proposed his typology in a 1946 ''Science'' article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both " qualitative" (which are described by his "nominal" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Of A Set
In mathematics, a partition of a set is a grouping of its elements into Empty set, non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a Set (mathematics), set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory. Definition and notation A partition of a set ''X'' is a set of non-empty subsets of ''X'' such that every element ''x'' in ''X'' is in exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets ''P'' is a partition of ''X'' if and only if all of the following conditions hold: *The family ''P'' does not contain the empty set (that is \emptyset \notin P). *The union (set theory), union of the sets in ''P'' is equal to ''X'' (that is \textstyle\bigcup_ A = X). The sets in ''P'' are said ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Binning
Data binning, also called data discrete binning or data bucketing, is a data pre-processing technique used to reduce the effects of minor observation errors. The original data values which fall into a given small interval, a '' bin'', are replaced by a value representative of that interval, often a central value (mean or median). It is related to quantization: data binning operates on the abscissa axis while quantization operates on the ordinate axis. Binning is a generalization of rounding. Statistical data binning is a way to group numbers of more-or-less continuous values into a smaller number of "bins". For example, if you have data about a group of people, you might want to arrange their ages into a smaller number of age intervals (for example, grouping every five years together). It can also be used in multivariate statistics, binning in several dimensions at once. In digital image processing, "binning" has a very different meaning. Pixel binning is the process of combin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Censoring (statistics)
In statistics, censoring is a condition in which the Value (mathematics), value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is ''at least'' 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 140 kg, after which it rolls over 0 and continues to count up from there. If a 160 kg individual is weighed using the scale, the observer would only know that the individual's weight is 20 modulo, mod 140 kg (in addition to 160kg, they could weigh 20kg, 300kg, 440kg, and so on). The problem of censored data, in which the observed value of some variable is partially kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aggregate Data
Aggregate data is high-level data which is acquired by combining individual-level data. For instance, the output of an industry is an aggregate of the firms’ individual outputs within that industry. Aggregate data are applied in statistics, data warehouses, and in economics. There is a distinction between aggregate data and individual data. Aggregate data refers to individual data that are averaged by geographic area, by year, by service agency, or by other means. Individual data are disaggregated individual results and are used to conduct analyses for estimation of subgroup differences. Aggregate data are mainly used by researchers and analysts, policymakers, banks and administrators for multiple reasons. They are used to evaluate policies, recognise trends and patterns of processes, gain relevant insights, and assess current measures for strategic planning. Aggregate data collected from various sources are used in different areas of studies such as comparative political ana ... [...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] |
Random Variate
In probability and statistics, a random variate or simply variate is a particular outcome or ''realization'' of a random variable; the random variates which are other outcomes of the same random variable might have different values ( random numbers). A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers. Procedures to generate random variates corresponding to a given distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Table
In statistics, the frequency or absolute frequency of an event i is the number n_i of times the observation has occurred/been recorded in an experiment or study. These frequencies are often depicted graphically or tabular form. Types The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events. The relative frequency (or ''empirical probability'') of an event is the absolute frequency normalized by the total number of events: : f_i = \frac = \frac. The values of f_i for all events i can be plotted to produce a frequency distribution. In the case when n_i = 0 for certain i, pseudocounts can be added. Depicting frequency distributions A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
