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)
“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)
“The Federal Constitution has stood the test of more than a hundred years in supplying the powers that have been needed to make the Central Government as strong as it ought to be, and with this movement toward uniform legislation and agreements between the States I do not see why the Constitution may not serve our people always.”
—William Howard Taft (1857–1930)
“I begin, then, with some remarks about ‘the meaning of a word.’ I think many persons now see all or part of what I shall say: but not all do, and there is a tendency to forget, or to get it slightly wrong. In so far as I am merely flogging the converted, I apologize to them.”
—J.L. (John Langshaw)