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:
“There are other measures of self-respect for a man, than the number of clean shirts he puts on every day.”
—Ralph Waldo Emerson (1803–1882)
“One point in my public life: I did all I could for the reform of the civil service, for the building up of the South, for a sound currency, etc., etc., but I never forgot my party.... I knew that all good measures would suffer if my Administration was followed by the defeat of my party. Result, a great victory in 1880. Executive and legislature both completely Republican.”
—Rutherford Birchard Hayes (1822–1893)
“The best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.”
—Alexis de Tocqueville (1805–1859)
“When any relationship is characterized by difference, particularly a disparity in power, there remains a tendency to model it on the parent-child-relationship. Even protectiveness and benevolence toward the poor, toward minorities, and especially toward women have involved equating them with children.”
—Mary Catherine Bateson (20th century)