An ordinal scale assigns values that encode an ordering of categories but not meaningful numerical distances between them. Any strictly increasing relabeling preserves the information in an ordinal scale. Examples include ranks and ordered response categories such as low, medium, and high.
Because only order is intrinsic, differences and ratios of the numerical labels are not invariant under permissible relabelings. The statistical median, quantiles, and rank-based methods are naturally compatible with ordinal data, while an arithmetic mean requires additional assumptions about how the labels represent distances.
