Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute.
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Ordinal scale in the context of Mohs scale
The Mohs scale (/moʊz/ MOHZ) of mineral hardness is a qualitative ordinal scale, from 1 to 10, characterizing scratch resistance of minerals through the ability of harder material to scratch softer material.
The scale was introduced in 1812 by the German geologist and mineralogist Friedrich Mohs, in his book Versuch einer Elementar-Methode zur naturhistorischen Bestimmung und Erkennung der Fossilien (transl. Attempt at an elementary method for the natural-historical determination and recognition of fossils); it is one of several definitions of hardness in materials science, some of which are more quantitative.
Ordinal scale in the context of Rank statistics
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
For example, the ranks of the numerical data 3.4, 5.1, 2.6, 7.3 are 2, 3, 1, 4.
Ordinal scale in the context of Ordinal utility
In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility.
For example, suppose George tells us that "I prefer A to B and B to C". George's preferences can be represented by a function u such that: