Components of Statistics
The theoretical side is largely based on a mathematical development of probability theory (see Probability Theory: An Outline) applicable to data, particularly the asymptotic properties of estimates (see Properties of Estimators) which lead to powerful theorems such as the Central Limit Theorem. The aim is to put many practical approaches to data analysis (see also Categorical Data Analysis; Multivariate Data Analysis: An Overview; Exploratory Data Analysis; Functional Data Analysis) on a sound theoretical foundation and to develop theorems about the properties of these approaches. The theories are usually based on a number of assumptions that may or may not hold in practice.
Practical statistics considers the analysis of data, how the data can be summarized in useful fashions, and how relationships between sets of data from different variables can be described and...