Scope of statistics

Some consider statistics to be a mathematical body of science pertaining to the collection, analysis, interpretation or explanation, and presentation of data,[5] while others consider it a branch of mathematics concerned with collecting and interpreting data. Because of its empirical roots and its focus on applications, statistics is usually considered to be a distinct mathematical science rather than a branch of mathematics. Much of statistics is non-mathematical: ensuring that data collection is undertaken in a way that allows valid conclusions to be drawn; coding and archiving of data so that information is retained and made useful for international comparisons of official statistics; reporting of results and summarized data (tables and graphs) in ways that are comprehensible to those who need to make use of them; implementing procedures that ensure the privacy of census information.

Statisticians improve the quality of data with the design of experiments and survey sampling. Statistics also provides tools for prediction and forecasting using data and statistical models. Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. Statistical consultants are available to provide help for organizations and companies without direct access to expertise relevant to their particular problems.

Statistical methods can be used for summarizing or describing a collection of data; this is called descriptive statistics. This is useful in research, when communicating the results of experiments. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and are then used for drawing inferences about the process or population being studied; this is called inferential statistics. Inference is a vital element of scientific advance, since it provides a means for drawing conclusions from data subject to random variation.

To prove the guiding theory further, these predictions are tested as well, as part of the scientific method. If the inference holds true, then the descriptive statistics of the new data increase the soundness of that hypothesis. Descriptive statistics and inferential statistics (a.k.a., predictive statistics) together comprise applied statistics.[9][verification needed]

Statistics is closely related to probability theory, with which it is often grouped; the difference is roughly that in probability theory, one starts from the given parameters of a total population to deduce probabilities pertaining to samples, but statistical inference moves in the opposite direction, inductive inference from samples to the parameters of a larger or total population.