normalities

Normality is a term used in several disciplines to denote different but related ideas about conformity to a standard or to a mathematical condition. In everyday language it refers to being normal or typical, but in technical contexts it has precise definitions that vary by field.

In statistics, normality describes data or distributions that approximate a normal (Gaussian) shape. Many statistical methods assume normality of residuals or errors. Assessing normality involves visual tools like Q–Q plots and tests such as the Shapiro–Wilk or Kolmogorov–Smirnov tests; departures from normality can affect inference and may lead to alternative analyses.

In chemistry, normality (symbol N) is a concentration measure defined as equivalents of solute per liter of solution. It is used in acid–base and redox reactions and depends on the reaction’s equivalent factor. Normality is related to molarity but differs in how the reacting species participate in the reaction; for polyprotic acids or multi-electron redox processes, normality can differ from molarity.

In topology, normality is a separation property of a topological space. A space is normal if any two disjoint closed sets can be separated by disjoint open neighborhoods. This concept is a fundamental axiom in point-set topology; metric spaces are normal, and several theorems (such as Urysohn’s lemma) apply in normal spaces.

In the social sciences, normality often concerns what is typical or expected within a culture or group. The term normalities in this sense is rarer than the use of norms; it can refer to recurring patterns of behavior or to interpretations of what is considered normal.