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Encyclopedia > Central tendency

In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. Central tendency is a descriptive statistic analogous to center of mass in physical terms. The term is used in some fields of empirical research to refer to what statisticians sometimes call "location". A "measure of central tendency" is either a location parameter or a statistic used to estimate a location parameter. A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... Various meters In classical physics and engineering, measurement generally refers to the process of estimating or determining the ratio of a magnitude of a quantitative property or relation to a unit of the same type of quantitative property or relation. ... Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. ... It has been suggested that this article or section be merged with Center of gravity. ... Empirical research is any activity that uses direct or indirect observation as its test of reality. ... In statistics, if a family of probabiblity densities parametrized by a scalar- or vector-valued parameter μ is of the form fμ(x) = f(x − μ) then μ is called a location parameter, since its value determines the location of the probability distribution. ... A statistic (singular) is the result of applying a statistical algorithm to a set of data. ...


There are several different kinds of calculations for central tendency, the kind of calculation depending on the type of data (level of measurement) for which the central tendency is being calculated. The level of measurement of a variable in mathematics and statistics is a classifcation that was proposed in order to describe how much information the numbers associated with the variable contain. ...


A list of measures of central tendency

  • Arithmetic mean - the sum of all measurements divided by the number of observations in the data set
  • Median - the middle value that separates the higher half from the lower half of the data set
  • Mode - the most frequent value in the data set
  • Geometric mean - the nth root of the product of the data values
  • Harmonic mean - the reciprocal of the arithmetic mean of the reciprocals of the data values
  • Generalized mean - the nth root of the arithmetic mean of the nth powers of the data values
  • Weighted mean - an arithmetic mean that incorporates weighting to certain data elements
  • Truncated mean - the arithmetic mean of data values after a certain number or proportion of the highest and lowers data values have been discarded
  • Interquartile mean - a special case of the truncated mean
  • Midrange - the arithmetic mean of the highest and lowest values of the data or distribution.

In mathematics and statistics, the arithmetic mean of a set of numbers is the sum of all the members of the set divided by the number of items in the set (cardinality). ... In probability theory and statistics, the median is a number that separates the higher half of a sample, a population, or a probability distribution from the lower half. ... In statistics, the mode is the value that has the largest number of observations, namely the most frequent value or values. ... The geometric mean of a set of positive data is defined as the product of all the members of the set, raised to a power equal to the reciprocal of the number of members. ... In mathematics, the nth root or radical of the non-negative real number a, written as , is the unique non-negative real number b such that bn = a. ... In mathematics, the harmonic mean is one of several methods of calculating an average. ... In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. ... A generalized mean or power mean is an abstraction of the arithmetic, geometric and harmonic means. ... In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted mean is calculated as Note that if all the weights are equal, the weighted mean is the same as the arithmetic mean. ... A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. ... The interquartile mean (IQM) is a statistical measure of central tendency, much like the mean (in more popular terms called the average), the median, and the mode. ... The midrange of a set of statistical data values is the arithmetic mean of the smallest and largest values in the set. ...

See also


  Results from FactBites:
 
Central tendency - Wikipedia, the free encyclopedia (313 words)
In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context.
Central tendency is a descriptive statistic analogous to center of mass in physical terms.
There are several different kinds of calculations for central tendency, the kind of calculation depending on the type of data (level of measurement) for which the central tendency is being calculated.
Measures of Central Tendency: Mean, Median & Mode (1170 words)
Notice that not all measures of central tendency are appropriate for all kinds of variables.
The rule is that, as the symmetry of a distribution increases, the three measures of central tendency converge on the same value.
As the asymmetry or skewness of a distribution increases, the three measures of central tendency diverge systematically.
  More results at FactBites »

 
 

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