Statistics, often regarded as distinct science rather than a branch of mathematics, is the study of data and uncertainty. Statistical techniques allow us to make conclusions, such as whether or not living near electricity pylons in dangerous, from sets of data. Statistics is also used in the design of effective experiments and in determining what data should be collected. For example, statistical techniques might be used to determine the frequency with which aircraft components should be tested for safety. Underlying these techniques is the assumption that these data are samples of a random variable that follows a probability distribution describing their behaviour. This module provides and introduction to probability and statistics. Axiomatic probability theory, including Bayes' Theorem, is discussed briefly. Key discrete and continuous probability modules (such as the binomial, Poisson and normal distributions) are introduced. Properties of expectation and variance are discussed. The Weak Law of Large Numbers and the Central Limit Theorem are covered before basic statistical ideas, such as statistical inference and hypothesis testing are introduced. Real world data are used to illustrate the theory.