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  Measures of Central Tendency Homework Help - K-12 Grade Level, College Level Mathematics

Introduction of Central tendency

In statistics, the term central tendency relates to the way in which quantitative data tend to cluster around some values. A measure of central tendency is any of a number of ways of specifying this central value. In practical statistical analysis, the term is often used before one has chosen even a preliminary form of analysis: thus an initial objective might be to "choose an appropriate measure of central tendency".

Both measure of central tendency and central tendency apply to either statistical populations or to samples from a population.

Basic measures of central tendency

The following may applied to individual dimensions of multidimensional data, after transformation, although some of these involve their own implicit transformation of the data.

  • Arithmetic mean - the sum of all measurements divided by the number of observations in the data set
  • Median - 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
  • Weighted mean - an arithmetic mean that incorporates weighting to certain data elements
  • Distance-weighted estimator - the measure uses weighting coefficients for xi that are computed as the inverse mean distance between xi and the other data points.
  • Truncated mean - the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded.
  • Midrange - the arithmetic mean of the maximum and minimum values of a data set.
  • Midhinge - arithmetic mean of the two quartiles.
  • Trimean - 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.

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