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Many statistical methods are available, including those in probability theory, sampling theory, mathematical statistics, econometrics, time series analysis, and actuarial science. Key concepts of statistics include hypothesis testing, descriptive and inferential statistics, sampling, and probability theory.

The field of statistics evolved from earlier applications in demography and econometrics into a broader discipline of information science. Probability theory and related concepts have played a key role. The probability theory of statistics is based on a formalized calculation of probabilities in a probability space consisting of a sample population, a sample space, and a set of observations or events. The probability space has the defining characteristics of the population and sample space being measurable and finite and the desired outcomes being observable.

Most statistics courses are taken in secondary education. This entails a survey and some statistical inference from empirical research. Some statisticians have degrees in mathematics, physics, or engineering, in addition to statistics, or may have a degree in a discipline such as biology. Statistics generally involves at least two disciplines: probability and mathematics. Descriptive statistics deals with (mostly numerical) data, while inferential statistics, e.g., statistical inference (using statistics as a tool), draws conclusions from data. The practitioner of statistics, however, may be a mathematician, engineer, or computer scientist. Quantitative analysts (quantitative sociology, business and economics) deal with data, and mathematical statistics.

Computer scientists usually have a similar path to statisticians, although the relationship between their disciplines is more direct than statisticians: computer science and statistics are both applied mathematics, and while computer science focusses on applications to computer science, statisticians generally apply mathematics to it. A computer scientist is concerned with the design and implementation of computer systems and with the use and analysis of statistical data. A statistician is concerned with the design, analysis, evaluation, and presentation of statistics, often for the purpose of computer science or engineering. d2c66b5586