Statistics and Natural Phenomena

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.[1][2][3] In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.

In statistics, a population is a set of similar items or events which is of interest for some question or experiment.[1] A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).[2] A common aim of statistical analysis is to produce information about some chosen population.[3].

In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. 

In mathematics, a set is a well-defined collection of distinct elements or members.[1][2][3] The elements that make up a set can be anything: people, letters of the alphabet, or mathematical objects, such as numbers, points in space, lines or other geometrical shapes, algebraic constants and variables, or other sets.[4] Two sets are equal if and only if they have precisely the same elements.[5].

Statistics are usually applied to Natural Phenomena when its nature is non-deterministic and therefore can not be predicted with certainty. Outstanding examples are atmospheric and hydrologic phenomena.

Scientists must be cautious about the concepts of Homogeneity and Heterogeneity of data when applying Statistics, so that meaningful conclusions can be obtained about the statistical universe/population selected.