normality

Normality is the state or condition of being normal, in the sense of conforming to a standard, norm, or typical behavior. The term is used across disciplines to describe objects, systems, or data that fit expected patterns, or to name a specific mathematical or scientific quantity.

In mathematics, normality is a property of a topological space. A space is normal if any two disjoint closed sets can be separated by disjoint open neighborhoods. If the space is also Hausdorff, it is often called a normal Hausdorff or T4 space. Metric spaces are normal, and normality supports results such as Urysohn’s lemma and Tietze extension. Normality can fail in spaces that lack suitable separation properties, and the behavior of products of normal spaces can be nontrivial.

In chemistry, normality (symbol N) is a measure of concentration defined as equivalents of solute per liter of solution. It depends on the reaction context: for acid–base or redox reactions, normality equals the molarity times the reaction relevance factor (the number of replaceable hydrogens or electrons transferred). Because the same solute can have different reactive capacities in different reactions, normality is less universally used than molarity or molality in modern practice, though it remains important in some titration contexts.

In statistics and data analysis, normality refers to the extent to which a dataset follows a normal (Gaussian) distribution. A normal distribution is bell-shaped and defined by its mean and standard deviation. Many statistical methods assume normality; tests for normality, such as Shapiro–Wilk or Kolmogorov–Smirnov, and visual tools like Q–Q plots are used to assess it. When data depart from normality, transformations or nonparametric methods may be applied.