Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments. Statistics
A statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained this experience through working in any of a wide number of fields. There is also a discipline called mathematical statistics that studies statistics mathematically.
The word statistics, when referring to the scientific discipline, is singular, as in "Statistics is an art." This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data, whose plural is statistics ("this statistic seems wrong" or "these statistics are misleading").
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth is not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the confidence a person has that a (random) event will occur. Probability
The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.