Central Tendency - Measures of Central Tendency

Measures of Central Tendency

The following may be applied to one-dimensional data, after transformation, although some of these involve their own implicit transformation of the data.

  • 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
  • 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 – 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 and, 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.

Read more about this topic:  Central Tendency

Famous quotes containing the words measures of, measures, central and/or tendency:

    “To have the fear of God before our eyes, and, in our mutual dealings with each other, to govern our actions by the eternal measures of right and wrong:MThe first of these will comprehend the duties of religion;Mthe second, those of morality, which are so inseparably connected together, that you cannot divide these two tables ... without breaking and mutually destroying them both.”
    —Laurence Sterne (1713–1768)

    “Away with the cant of “Measures, not men!”Mthe idle supposition that it is the harness and not the horses that draw the chariot along. No, Sir, if the comparison must be made, if the distinction must be taken, men are everything, measures comparatively nothing.”
    —George Canning (1770–1827)

    “Friends serve central functions for children that parents do not, and they play a critical role in shaping children’s social skills and their sense of identity. . . . The difference between a child with close friendships and a child who wants to make friends but is unable to can be the difference between a child who is happy and a child who is distressed in one large area of life.”
    —Zick Rubin (20th century)

    “Editing should be, especially in the case of old writers, a counseling rather than a collaborating task. The tendency of the writer-editor to collaborate is natural, but he should say to himself, “How can I help this writer to say it better in his own style?” and avoid “How can I show him how I would write it, if it were my piece?””
    —James Thurber (1894–1961)