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:
“Those who, while they disapprove of the character and measures of a government, yield to it their allegiance and support are undoubtedly its most conscientious supporters, and so frequently the most serious obstacles to reform.”
—Henry David Thoreau (1817–1862)
“However much we may differ in the choice of the measures which should guide the administration of the government, there can be but little doubt in the minds of those who are really friendly to the republican features of our system that one of its most important securities consists in the separation of the legislative and executive powers at the same time that each is acknowledged to be supreme, in the will of the people constitutionally expressed.”
—Andrew Jackson (1767–1845)
“There is no such thing as a free lunch.”
—Anonymous.
An axiom from economics popular in the 1960s, the words have no known source, though have been dated to the 1840s, when they were used in saloons where snacks were offered to customers. Ascribed to an Italian immigrant outside Grand Central Station, New York, in Alistair Cooke’s America (epilogue, 1973)
“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)