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In statistics, a central tendency (or, more commonly, a 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, ISBN 0-8039-4007-6 p.2〕 It may also be called a center or location of the distribution. 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 central 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 ISBN 978-0-19-954145-4 (entry for "central tendency")〕〔Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP for International Statistical Institute. ISBN 0-19-920613-9 (entry for "central tendency")〕 The central tendency of a distribution is typically contrasted with its ''dispersion'' or ''variability''; dispersion and central tendency are the often characterized properties of distributions. Analysts may judge whether data has a strong or a weak central tendency based on its dispersion. ==Measures of central tendency== The following may be applied to one-dimensional data. Depending on the circumstances, it may be appropriate to transform the data before calculating a central tendency. Examples are squaring the values or taking logarithms. Whether a transformation is appropriate and what it should be depend heavily on the data being analyzed. *Arithmetic mean (or simply, 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. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely. *Mode – the most frequent value in the data set. This is the only central tendency measure that can be used with nominal data, which have purely qualitative category assignments. *Geometric mean – the ''n''th root of the product of the data values, where there are ''n'' of these. This measure is valid only for data that are measured absolutely on a strictly positive scale. *Harmonic mean – the reciprocal of the arithmetic mean of the reciprocals of the data values. This measure too is valid only for data that are measured absolutely on a strictly positive scale. *Weighted mean – an arithmetic mean that incorporates weighting to certain data elements. *Truncated mean (or trimmed mean) – the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded. * *Interquartile mean – a truncated mean based on data within the interquartile range. *Midrange – the arithmetic mean of the maximum and minimum values of a data set. *Midhinge – the arithmetic mean of the two quartiles. *Trimean – the weighted arithmetic mean of the median and two quartiles. *Winsorized mean – an arithmetic mean in which extreme values are replaced by values closer to the median. Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space. In addition, there is the *Geometric median - which minimizes the sum of distances to the data points. This is the same as the median when applied to one-dimensional data, but it is not the same as taking the median of each dimension independently. It is not invariant to different rescaling of the different dimensions. The Quadratic mean (often known as the root mean square) is useful in engineering, but is not often used in statistics. This is because it is not a good indicator of the center of the distribution when the distribution includes negative values. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「central tendency」の詳細全文を読む スポンサード リンク
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